With due respect to Dr. Adequate, I think I can point out where your math went wrong. It's right around here:
So if we figure a mammal breeds on average once a year that only allows 200 - 300 million generations for all those consecutive mutations to occur and propagate.
If a beneficial mutation occurs say once every million times an animal reproduces
You seem to be neglecting to include the fact that every pairing (mating) of genetic material results in at least a few mutations or errors. There may also be some errors that occur during the early stages of gestation, leading to changes within most of the cells of the subsequent animal. Also, many animals give birth to more than one child at a time, increasing the number of mutations occurring. Add to that the fact that every species has more than one breeding pair, in fact, quite possibly millions of breeding pairs, meaning that millions or billions of mutations occur in every breeding/birthing season, per species, and any really bad mutations will never make it to term, or will die shortly thereafter, making the beneficial mutations much more likely to rise to the top, as it were.
So, every child born has some mutations, some help, some hurt, many do nothing overt at the moment. These mutants (every animal ever born is a mutant) then breed with other mutants, adding more mutations. In species that are not monogamous, this mutational spread (or genetic drift) increases, and if a mutation helps an animal breed, even a little bit, that mutation gets spread even farther.
You're not taking into account the sheer number of mutations that occur nor population size considerations. I think you're missing out natural selection as a way of weeding out mutations as well, but I'm not quite sure of this since you didn't explain enough.
I may be explaining it poorly. I thought genetic drift is when the proportion of alleles expressed in the population changes due to reproductive chance rather than through actual selection. So, if a species is not monogamous, an allele can be increased in proportion by a carrier of that allele breeding more (by chance) than a non-carrier, rather than a carrier of the allele actually having a reproductive benefit due to that allele.
For example, eye color is generally not going to enhance or detract from your ability to mate in general, but if a blue eyed male happens to have sex with a lot of different females in any given breeding season who then produce some blue eyed kids, the proportion of blue eyes will increase more than if that blue eyed male had only had sex with one female during that breeding period.
And that this is independent of actual beneficial mutations that will give the individual an actual boost in reproductive success. Having an actual boost will increase the proportions more than merely chance in the previous example.
Micro evolution (small changes WITHIN species) is based on observable evidence
But macro evolution is just a lot of micro evolution. If you can have small changes, what stops those small changes from accumulating? What creationists who accept micro evolution have to do is offer some mechanism that stops micro evolution from continuing. After all, one penny isn't much, but keep adding pennies and eventually you've got a pile of real money.
Macro evolution is a consequence of micro evolution, unless you can come up with a mechanism that limits it. So far, none have been found, so if you're the first, you'll get a nice shiny Nobel Prize for your efforts.
I also don’t think that observed natural selection is evidence of macro evolution since natural selection eliminates information but does not add new information.
Natural selection weeds out the bad mutations, true, so while it doesn't add any new information, it does make sure that any new information added is good or at least neutral. It's natural selection PLUS mutation that gives evidence of evolution (macro or micro, you end up at the same spot).
What evidence (observation)points to an animal developing a new organ or growing a new limb and then passing it on to future generations?
The best evidence for macro evolution occuring is in the fossil record. But you seem to be confusing what actual evolution would do versus what sci-fi movies and creationists say evolution should do.
For one thing, a brand new limb does happen, look at recent amphibian problems as evidence. True, these are disadvantageous mutations, and are usually quickly weeded out, but any large scale change like that is more often than not going to be disadvantageous. Most evolution is, like American football, a game of inches. You don't go from point A to point B by strapping on a jet pack and getting there in one giant leap, you take steps, eating away the miles slow and steady. Often, evolution just modifies what's already there, rather than making something completely new.
I simply base this on the fact that we have observed trillions of pairings among animals and humans in the last thousand years and not once has a single beneficial and lasting mutation in a human or animal been observed.
Animal husbandry as a science would disagree with you. It might not be big enough changes for you, but look at all the breeds of dogs that come from a wolf, or all the types of cow we have, which came from one particular ancestor species (I think). A wolf couldn't go down into burrows and fight a badger. Dachshunds can, and this is based on small changes being added to over many many generations. True, this is not natural selection, but artificial selection, but since you've already accepted mutation and natural selection, what theoretical mechanism would have stopped wolves from evolving into dachshunds if they got stuck in an environment that highly favored their ability to go after badgers?
I would also disagree with beneficial mutations not having been observed in nature, but as I've said, changes are small and for something to build up, you often need to have a new environment, or have a niche open up due to something else dying off. Humans are not going to evolve as much since we have technology and intellect to counteract much of what nature throws against us. As for other animals, even 1000 years is often not long enough to see big changes since generation lengths are quite long. This is why most evolutionary studies have to do with bacteria and thigs that reproduce very quiuckly, and we have definitely seen beneficial mutations in bacteria. In fact, it's exceedingly easy to get beneficial mutations in bacteria...all you have to do is drastically change the environment, and viola, you'll see most individuals die off, and the ones that are left are the ones that had a mutation that was not present in the others and helped them survive.
Considering the trillions of variations that would have been necessary in only 600 million years
Maybe I missed it, where do you get this number? As far as I know, life has had at least 3.5 billion years to work with.
I imagine it must be frustrating to time and time again find the same type of dinosaur, fish, bird or plant fossils here and there but not be able to find an equal number of (or even a few) fossils for the billions of intermediary species.
How would you know an intermediary species? Are you expecting to find a species that has a T. rex head and a brontosaurus body? If you foudn that, again, you'd get a Nobel prize for destroying much of evolutionary theory (assuming it was legitimate). What you find, if you actually look, is a gradual progression from one type of animal or plant or dinosaur to manyh different ones that are obviously related. Just recently, they found an ancestor of T. rex that was quite small, but had the same morphology as the T. rex we all know and love. In fact, they often find different species and intermediate animals...especially when they use evolutionary theory to predict where to look to find exactly those species. (Rememeber, even intermediate animals belong to one species or another, you're never going to find an animal that is in between two species but not part of a species itself.)
Humans selected the qualities they wanted and bread only the animals that exhibited those qualities.
Yes, but where did those qualities come from in the first place? They were mutations. Humans artificially constrained the environment to get an outcome they wanted, but environments in nature can and do do the same thing.
And if humans ever stopped controlling the breeding, dogs would return to their more primitive forms.
Proof? We have wild dogs in many places throughout the world, and while they are often mutts, rather than a continued lineage of, say, golden retreivers, they are most definitely not wolves. But, this just begs the question of when a "breed" becomes a "species." Is a lion just a breed of tiger, or vice versa? Are there more differences between a chihuahua and a wolf or a wolf and a coyote? Are coyotes just a breed of wolf, since they can interbreed? The problem is, we're looking at a very small snapshot of a process that takes a long time. Come back in a million years and I'll bet the things we call dogs wil not be able to breed with the things we call wolves...though you may have trouble recognizing either one.
How many evolutionary steps did it take for dinosaurs to become birds?
According to evolution, zero, since birds would then still be dinosaurs. But I understand you mean at what point does what we all recognize as a dinosaur become what we all recognize as a bird? Well, that depends because as you get closer to the transition point, what one person would call "still a bird" another person would call "still a dinosaur." The classic example of archaeopterix...is it a bird or a dinosaur? Evolutionarily, it's still a dinosaur, but is it also a bird, as modern birds are? That's more a judgement call than a scientifically investigable question since it requires someone to decide how many bird features they need for it to be considered a bird.
Surely there must have been more intermediary steps between them than there are species of dinosaurs.
But, unless a species of dinosaur just completely died out, tey're all intermediary steps between it's ancestor species and it's daughter species. Each intermediary step is also a species, what you have to look at, and all we can really look at, is the morphology of the species and it's placement in time. If we look at the evolutionary line of birds, we see certain dinosaur species that are smaller and lighter than previous species, ones that have modified scales called feathers, ones that have more hollow pneumatic bones than previous species, and finally, species we invariably classify as birds. Each one is a species in its own right, and many of them have been found in abundance, and placed in time, it provides a very obvious transition. The fact that we don't have every step is due to the fact that fossilization is a very rare event. It requires very exact conditions to stop decay and allow mineralization. The fact that there are so many intermediary species being found is, frankly, amazing to me and is a strong indicator that we're on the right track.
Think of the trillions of mutations and the countless generations spent isolating those traits through natural selection.
Well, bottlenecks, extinction and isolation would serve to stabilize some species' traist very quickly, while others may take a longer time, which is why some groups of animals don't change a lot over a long period of time (alligators and crocodiles for two).
Or can someone explain why evolution appears to have stopped or slowed?
It appears to have stopped or slowed because you're looking through millions of years of history, and then only hundreds of years of present, and trying to correllate the two and doing it incorrectly. When you see a museum exhibit with a fish fossil, then an amphibian fossil and it says, it took X million years to go from the first type of species to the second, and then you look around and say, I haven't seen any change like that recently, you're getting the time scales wrong. This is very easy to do when the numbers get big. If it takes one million years for a big change to develop and become stabilized, why would you expect to have seen it? Humans have only been around a few hundred thousand years (at most) and science has only been around a couple thousand years (again, at most) so why do you think looking at a snapshot gives you a good feel of the entire movie?
According to evolution each fossil we find in separate locations should statistically be slightly different
This is what we find, if by location you mean time. If we look at one stratigraphic layer, we see animal X. If we look a few layers above or below that, we see an animal that looks like X, but not quite. The problem is, as I said above, fossilization is extrememly rare. There are quite definitely many many species that have never been fossilized and so are lost completely to our knowledge. What we have are snapshots, but we can place the snapshots in order based on the layers they werw found in, and by looking at the snapshots in order, we see an obvious sequence. It's like taking every millionth frame of a movie, you could place them in order based on where you cut them out of the reel, and you could see the progression of the movie despite not seeing every frame. (Comic books often exploit this very fact, they don't draw every motion, just the relevant ones.)
intermediary species with partially developed organs or bones.
If this is what you're looking for, you'll never find it. If you did, you'd win a Nobel Prize for completely changing how we view evolution. If an animal were born with a partially developed organ or bone, they would more than likely not survive. The only way we would get a "sort of" partially developed organ is if the ancestors of that species had an organ that was no longer very useful. (i.e. appendix in humans) Otherwise, ever organ and bone will be fully developed to do a task, it will just be slightly modified from a previous organ or bone.