In order for that to disprove evolution (and geology, as well), it would have to be established that no explanation within current geology is possible, and I'm not aware that that case has been made. Failing that, it is a phenomenon that is being studied:
Source
Missing links are in no way problematic for evolution, as evolution doesn't predict that we're able to find every fossil, nor that a fossil of every species was made in the first place. Obviously, finding a fossil depends on (1) how many fossils were made (and fossilization is very rare), and (2) our ability and resources devoted to finding them. Neither of those two factors has anything to do with the essential elements of evolution (common descent, mutations, natural selection, etc.).
Same as above. It's a problem to solve, and no one has shown that this disproves evolution; generally, the best one could do is to ask, "How could the evolution of flowers possibly happen?" But that is a question, it's not a disproof of evolution.
I don't know the specifics of what you're talking about, but carbon dating only has a limited range of dates that it works for, so I don't know what the problem is. And, again, a mystery or an unsolved question is not a refutation.
That's pretty vague. Exactly what is he talking about, and specifically, (1) what is his claim, and (2) what is the evidence that sufficiently demonstrates his claim?