Maybe nothing except a plethora of incredibly beautiful women, as is the case in Iceland. ;-) Or, more seriously, problems such as hip displasia, as occurs when dogs become too inbred.
BTW, this article doesn't actually tell us whether these colonies are truly isolated, or if there's a possibility of intermingling between adjacent islands. It seems to me that if these birds are island-hoppers, there's no reason to expect that they only hop to un-colonized islands.
If X amount of genetic changes occur in 3000 years, then how many more changes would occur in 3 million or 300 million years?
Who knows -- certainly neither of us does. If I had to guess, I'd say that the changes over 3 million years would be minor, primarily because I think the colonies would intermix over time. Nobody's claiming, after all, that this species all of a sudden appeared only 3000 years ago -- I suspect that the silvereye species has been around for a long time.
At any rate, this is pure guesswork. It is certainly not a "test" of evolution to attempt to extrapolate these results to arrive at some pre-determined conclusion. At best, I think one can claim that this is nothing more than a "test" that proves obvious fact that children bear the genetic characteristics of both parents.
I would speculate that various genetic processes occur at different rates. If there were a diffusion-like drift (I haven't checked to see if this is a good model.) things would happen at all time scales. The non-independence of mutations and the effects of selection make analysis difficult.
We have a few examples of genetic changes from 300-400 million years ago - the shark and the coelacanth. The answer is ZERO. Speculation is not science, evidence is science and you can speculate all you want but without evidence you got nottin'.