Scattered comments:

1) It's not that some illusions give hints as to how human cognition works; all of them do, because that's what makes it an illusion: a deviation from accuracy that is used as a usually-harmless shortcut.

2) All inference, not just perception, is based on incomplete information. MacKay says (quoting someone far before him), "To make inferences, you must make assumptions."

3) I don't think it's most accurate to say that the brain prefers wrong to uncertain. Rather, it prefers sometimes-wrong to always-uncertain. The heuristics it uses will usually be right, giving the benefit of being able to make use of greater (assumed) knowledge of a scene, at the cost of being wrong in a few rare cases. This is better than remaining non-committal, such as what would result from only using an Occamian heuristic.

4) The spinning dancer illusion doesn't work because of the detail; it works because it strips away all of the hints your brain normally uses to disambiguate a scene (such as light gradients, relative sizes, etc.)

5) Here's another great multi-stable perception illusion -- with something like 6 possible perceptions.

6) Great article! I'm also writing one about the non-obvious constraints that general intelligence must adhere to.

ETA: So I guess you guys want more of this kind of comment and less of the other?