What mutations are needed for a particular trait (e.g. wings) to arise?

In science, there is ALWAYS room for new explanations. The falsifiability of scientific theories requires this. But for science to consider new explanations you have to (1) actually provide one and (2) provide evidence that your explanation is better than the mutation alone one.

What you seem to be suggesting is that natural selection would have some kind of foresight as to what might become advantageous. It doesn't. Rather, certain individuals carrying certain mutations are more likely to leave more offspring, leading to those mutations becoming more common in a population. There is nothing magic about mutations. Natural selection merely makes individuals with a certain mutation be more reproductively succesful, while individuals with other mutations are less reproductively successful.

There are certainly a good deal of "errors" that could happen. Some small (ie one base affected) and some large (thousands of bases inserted, deleted and altered, all in one go). In order to calculate the likelyhood of one being beneficial one would probably first have to determine empirically the fraction of mutations that are positive and those that are negative. I've only seen something similar to this being done for simple point-mutations, which does not reflect what really happens in real life. As far as I'm aware, a realistic model for this has not been done so far. But hey, there are thousands of articles published daily(?), so who knows? If you find one that does go into detail about this, I'd certainly be keen to know.That's a bit of a non-answer, I suppose. So the absense of any kind of research into that area would mean that any kind of discussion concerning it would be speculative.

I would say that in some cases it is possible to predict with reasonable accuracy whether or not a certain mutation is beneficial/harmful. Since we know that certain genes are absolutely vital for survival, mutations that render these genes non-functional will by necessity be harmful (to conceive of such a mutation is easy - just delete the entire gene). To predict if a mutation would be beneficial might be more difficult, but given that an often given definition of a mutations is something like "A change in a DNA sequence", I'd like to give an example of a mutation that is highly likely to be beneficial in a certain environment: it is well known that bacteria often acquire resistance to antibiotics via horizontal gene transfer. Thus, a bacterium that has acquired an antibiotic resistance gene (which should fit the definition of a change in DNA sequence) would most likely have acquired a beneficial mutation (assuming that said antibiotic is common in it's environment and that the bacterium was not already resistant).

Studies have been performed to asses the impact mutations have on the fitness of organisms. Relative to wild-type individuals, fitness in mutants is almost invariably lower. This sort of makes sense, since there are more ways for a protein not to work then there is for it to work (all this assumes that the mutation happens in a sequence that codes for a protein in the first place). Experiments such as these do support the assertion that most mutations are harmful.The problem with these experiments, as we both would probably agree, is the one of that filter you mentioned. These mutations were harmful in the environment in which they were selected for. They might not have been in another environment. Saying that, even if the environment changed, it would most likely still be true that most mutations are harmful.

If evolution was true, we would not expect to observe extraordinary changes (such as you seem to use the term here). While some mutations might produce some wicked instant new features (such as hens sprouting teeth) this is because the pathways involved in teeth formation are usually swiched off (and also revealing that the ancestors of hens had teeth). Insisting that the observation of extraordinary new feaures have not been done and concluding that this somehow falsifies evolution (if that is what you are doing) is simply a strawman.