I'll personally agree with these comments:
In general, people who seek new skills and challenges get better over time
I agree with the idea that experience does not necessarily equal skill, and that skill in the context of gaming is open to interpretation.
Sometimes even vast experience can be exceeded by skill, particularly if it is also extensively varied experience, though it rarely surpasses ego. Just sayin'.
One of the veteran players was a great powergamer, but could not roleplay to save his life.
Experience is certainly not skill, which requires experience but also intelligence and wisdom (strange how many D&D terms made it into that).
Experience is one route to skill
As for me, my general observation about people, their level of skill (at anything, certainly not just games) is that if a person approaches whatever they are doing with seriousness, interest, commitment, and desire, then experience tends to assure they become better at what they do, generally speaking.
If they approach whatever they are doing with an air of mediocrity, lack of interest and commitment (it's just a job, I just have to put in enough effort to get by), and no real sense of seriousness (and I don't mean drop dead serious all of the time, humor and a philosophical attitude often makes a better practitioner than not) then experience will probably not add to or augment that person's general skill set or level of capability.
As to your last question, I think that is less a question of skill directly, but one of how flexible one is at adapting to and employing new skill sets and how willing one is in critically analyzing current skill sets and therefore modifying those current skills sets in an innovative and creative manner.
I personally am not a big advocate of the modern idea of "Expertise" because personally I associate too much of what passes for the underlying assumptions regarding modern expertise to be counter-reactionary (or reactionary, pending on how you want to employ the terms) towards innovation, flexibility, adaptability, and experimentation (that is towards the kind of radical experimentation that might lead to wholly new and innovative methods, techniques, and capabilities in whatever field or discipline is being discussed). That is, to me, too much of modern expertise is merely a stifling set of rigid ideas and beliefs that might, or might not be true at all, but which are far too often defended to the death as if they are the only ideas that could possibly be true.
However, that being said, I do recognize that there must be an agreed upon standard of what constitutes true expertise, or anyone could easily claim to be an expert on anything for any reason whatsoever (expertise then becomes nothing more than a competing set of subjective claims with no real evidentiary base of disclosure), and personally speaking, I think this also occurs far too often in our culture. So to me expertise is sort of caught on the horns of a Modern Dilemma, a horn too large to be easily employed in one case, and a horn too small to be really useful on the other.
The same basic standard applies, I would say, for individuals (in whatever it is they endeavor to excel) - you want them to know enough to be assured of what they do, but never enough that they stubbornly refuse to examine, test, and potentially employ new, viable, and especially valid techniques when they appear. Stick to what you know when it works, never be afraid to test what is new to see if it may work better (and it may, or may not, but you cannot truly know without critical examination).
So I would say that innovation may be a component of skill, or may not be, but I suspect it is a skill in its own right, and that when combined with other elements such as capability, intelligence, wisdom, foresight, and creativity can lead to Genius. But that's another matter, for genius far exceeds mere skill alone, though if truth be told, there is little possibility of genius without real skill.
I do definitely agree with the point of Einstein that when it comes to innovation imagination is more important than intelligence, and with the Bible that when it comes to the world Wisdom is better than gold.
Exposure is an important point to consider when regarding skill as well, as others have already mentioned or implied. A limited base of exposure leads to a limited base of potential insights when considering how to address any problem. But then again as Hobo implied, much depends upon the ultimate objective towards which one is working. There is indeed depth expertise, as well as width expertise, and the range and effectiveness of either depends a lot upon what is the actual objective? Is it to be extremely good and specialized at one thing (not to my individual taste or personal proclivity, but then again you need people who are extremely good at narrow efforts, especially in modern, technical societies, and possibly also in many game settings), or is it to be functionally good at many things, such as the Renaissance Man? Each has definite advantages and definite disadvantages.
As a last point on this issue I would also say that skill and experience are not necessarily related. I have seen many people who are naturally skilled at a thing (the talented or ingenious amateur), and exceed those with far greater ranges of experience, however if skill and experience are combined together seamlessly in the same individual, then that person becomes formidable in capability indeed. And I should also mention this point, being highly critical of the faults of others or of a system (not just a gaming system) in no way implies either skill or expertise. Criticism alone in no way implies anything about skill or capability. If on the other hand the criticism is valid it may have been developed or resulted through skillful observation or through hard-won experience, but then again being a good critic and a valid critic may just imply a separate type of skill. Being critical can be a type of skill all by itself, unrelated to other issues. Or out another way, you can be a very good critic of music, and be a really lousy musician. I think that should be pointed out because often time sit seems to me that the idea oaf being a good critic is conflated and confused with being a skillful practitioner of whatever it is one is criticizing. These may be related functions, then again, they can be totally unrelated functions. To me though, among certain population sub-sets, such as Geeks and Nerds for instance, this a priori assumption, that being a good critic somehow naturally equates with being a good practitioner, is far more often than not a critically unquestioned premise, and very little more than that.
As a personal observation it appears to me that the older editions of the game had the more "Specialized Character Classes," (specialized as in unique, fixed, and not exchangeable in function) and the more Modern iterations have been moving more and more towards the multi-functional "Renaissance Type" of character, where capabilities are overlapping or exchangeable, if not in name then in function.
Anywho I gotta bug to go somewhere.
It's an interesting set of questions to consider.
