What cases in nature are the most troublesome for scientists to reconcile with the theory of evolution by natural selection? Are there any at all? Or are they so numerous that a top-10 list would be in order to get started?
It seems to me that the case of ornaments for sexual selection is troublesome, because I found two competing explanations: one is Fisher's runaway explanation, and the other says an ornament advertises fittness and good genes because its owner is able to survive despite being handicaped by it. But maybe scientists do not consider ornaments troublesome, and it is only what scientists find troublesome that I'm asking about.
I think your example beautifully demonstrates the disconnect between your standpoint and that of a scientist. They are
many questions in Evolutionary theory which are either unanswered, or where the potential answers have not been satisfactorily resolved one way or the other. You've given one example, I can throw in some more - the nature of pre-cambian evolution, why and how humans developed such remarkable brains, and naked skins, what patterns of rate change typify evolution, how much do random events influence the large scale pattern of evolution, etc.
However, no scientist is going to consider these "troublesome to reconcile with the theory of evolution" (although some might quibble with the 'by natural selection' bit) because they're unanswered questions
within the settled question of whether things evolve at all. To give an analogy, historians of the second world war will argue vociferously over how important this battle or that battle was, how much technology played a role, exactly how many Jews died in the camps etc., etc. but no serious 2nd world war historian is going to deny that there was a second world war, or that Britain, Russia and the US where on the same side fighting the Germans or that vast numbers of Jews (and Gypsies and homosexuals) were killed by the Germans in concentration camps, etc.