There's a controversy
I guess the most popular controversy surrounding bats since "blood-sucking" vampires--Please, let's lay that one to rest. Vampires drink or lap blood, they don't suck. They lap like a cat, turning their tongues under--The biggest controversy at the moment is on the phylogeny of bats and whether they evolved once or twice. One of the big arguments against diphyly, separate evolution of megabats and microbats, is the supposed difficulty of evolving flight twice. On the face of it that seems to be a specious argument. If flight could evolve once, why couldn't it evolve twice? It's not that difficult to stretch your arms and fingers out, invent sonar and ultrasounds. However, the current resolution is to have all bats monophyletic, evolved from a common ancestor.
The naming of bats
I've already alluded to the difficulty of vernacular names. Even the name "bat" is not applied universally. In Spanish, "bat" is "murceliego", in Portuguese "morcego", in German "fledermaus" in French "chave souris", and in Jamaica it's rat bat ("rot bot"). So, there's a real problem with nomenclature. For bats, as for all animals, the earliest nomenclature that we follow is Linnaeus' Tenth Edition of "Systema Naturae", published in 1758. In "Systema Naturae" bats were a subdivision of Primates, based primarily on the similarity of the reproductive organs. With pectoral mammae and pendulous penis, bats reminded Linnaeus of little people with wings. Linnaeus recognized seven species of bats in the world. Now we list about 1,000.