Sometimes Bayesianism is proved, other times it is acknowledged to have known flaws. Sometimes it may be completely compatible with Popper, other times it is dethroning Popper. It seems to me that perhaps Bayesianism is a bit underspecified. I wonder why they haven't sorted out these internal disputes.

There are disputes among the Bayesians. But you are confusing different issues. First, the presence of internal disputes about the borders of an idea is not a priori a problem with an idea that is in progress. The fact that evolutionary biologists disagree about how much neutral drift matters isn't a reason to reject evolution. (It is possible that I'm reading an unintended implication here.)

Moreover, most of what you are talking about here are not contradictions but failure to understand. That Bayesianism has flaws is a distinct claim from when someone talks about something like Cox's theorem which is the sort of result that Bayesians are talking about that you refer to as "Sometimes Bayesianism is proved"(which incidentally is a terribly unhelpful and vague way of discussing the point). The point of results like Cox's theorem is that if one very broad attempts under certain very weak assumptions to formalize epistemology you must end up with some form of Bayesianism. At the same time it is important to keep in mind that this isn't saying all that much. It doesn't for example say anything about what one's priors should be. Thus one has the classical disagreement between objective and subjective Bayesians based on what sort of priors to use (and within each of those there is further breakdown. LessWrong seems to mainly have objective Bayesians favoring some form Occam prior, although just what is not clear.) Similarly, when discussing whether or not Bayesianism is compatible with Popper depends a lot on what one means by "Bayesianism", "compatible" and "Popper". Bayesianism is certainly not compatible with a naive-Popperian approach, which is what many are talking about when they say that it is not compatible (and as you've already noted Popper himself wasn't a naive Popperian). But some people use Popper to mean the idea that given an interesting hypothesis one should search out for experiments which would be likely to falsify the hypothesis if it is false (an idea that actually predates Popper) but what one means by falsify can be a problem.