For a change of pace, Jerry Coyne at Why Evolution Is True turns his attention to the issue of evolution. In a post titled “What would disprove evolution?,” he observes: “If evolution is a scientific theory worth its salt, then there must be some conceivable observations that could show it to be wrong.” True!
Two comments on Coyne’s list. He writes, “Here are some of those conceivable observations:”

• Fossils in the wrong place (e.g., mammals in the Devonian). If the fossil record were all out of order like this (a single anomalous fossil might not overturn everything, of course, since it could be in the wrong place for other reasons), we’d have to seriously question the occurrence of evolution.

Fossils are found in the “wrong place” all the time (either too early, or too late). Paleontological theory, however, allows for such devices as “ghost lineages” to repair the damage; see ENV’s coverage here and here.

• Complete discordance between phylogenies based on morphology/fossils and on DNA. While individual genes can show discordance by lateral transfer — rotifers, for example, have incorporated into their genome from DNA from very unrelated organisms, and this is also common for bacteria. But lateral transfer of genes, as opposed to their direct descent from parent to offspring, is relatively uncommon. So, for example, if we sequenced the genome of a blue whale and found that on the whole the species was more closely related to fish than to mammals, we’d have a serious problem for the theory of evolution.

Again, discordance between molecular and anatomical phylogenies is commonplace in systematics; see here.
But we expect Coyne is able to handle these anomalies via his shock-absorbing adjective “complete,” which allows an indefinitely large range of possibilities, short of “complete” discordance (whatever that means).