Biogeographical anomalies -- apparently ‘closely-related’ and pretty immobile organisms found on different continents, something like Orchidis prettiflowerii subspeciesalpha in India and Orchidis prettiflowerii subspeciesbeta in North America. Or species of lizard on a 4myo volcanic island in the Pacific whose nearest presumed relatives live on islands off the west coast of Africa. Again, an odd case might have some explanation within evolution; but a large number of examples would be pretty damning. After all, evolution is the reason for the biogrographical distributions we see, but there’s no reason -- other than that -- why prehensile-tailed monkeys, say, should only be found in the New World.
Careful there, DT. Biogeography has a LOT of this kind of anomaly. Ex. giant land tortoises are found on Aldabra Atoll in the western Indian Ocean (and formerly on nearby islands; species:
Geochelone gigantea) and the Galapagos (species:
Geochelone elephantus) on the other side of the world. The small tree genus [i]Trochetiopsis[i] contains three species - all endemic to one tiny flyspeck
isle perdu in the Atlantic (St. Helena). Its nearest living relative is the genus
Trochetia, endemic only to Mauritius in the Indian Ocean - a really looong way away. There's lots of examples like this.
A better biogeographic "falsification" would be if two species morphologically and ecologicaly similar were adjacent to each other spatially but shared no genetics - like finding
Thylacinus cynocephalus sharing overlapping ranges with
Canus lupus. Or two species of squirrel-niche critters sharing the same North American beechwood habitat that were from completely different subfamilies. You get the idea.
I do like the rest of your examples, tho'.