An excellent post, nwr, covering many important ideas concisely and understandably. I'll try to add some detail that hopefully you'll find interesting:
When there is very little diversity present, the factors that decrease diversity won't have much effect, since there isn't much to decrease. Thus the factors that increase diversity will tend to dominate. Conversely, if there is a lot of diversity, then the factors that decrease will tend to dominate.
Dobzhansky demonstrated this in the 1950's with fruit fly experiments. He took several pairs of fruit flies from a large colony and used them to seed new colonies - creating a series of severe bottlenecked populations. These bottlenecked populations consistently and rapidly became more phenotypically variable than the founder population, which stayed relatively stable. (This is one of those classic papers I wish I could find on-line...)
If a species is already well adapted to its environment, then it is to be expected that most mutations will be negative or neutral. This is a bit like the saying "if it ain't broke, don't fix it." If things are working reasonably well, and something changes, the change is more likely to be for the worse.
Yes - this is called "normalizing" or "neutralizing" selection; that is, selection that maintains the status quo. Most species can be thought of as "optimized" given their long evolutionary histories - which is why we rarely directly observe beneficial mutations.
If the environment changes in such a way that the species is less well adapted to the changed environment then, as the paragraph above indicates, there will be more room for improvement so more of the random mutations will be beneficial.
That's when normalizing selection ceases - with a change to the environment. This is why our examples of recent beneficial mutations often are the result of new environments being created by man - mutations to resist pesticides or antibiotics, or to use a synthetic like nylon as a food source.