One mistake I noticed when tutoring a high school student was what I might call "failure to take seriously the rules."

We were studying Geometry, and many times the student would make a big assumption (e.g. the angle is 90 degrees) without noting or questioning whether it was true.

When I'd ask him about it, he would say "Look at it, it must be 90 degrees!" or "If it's 90 degrees, then I can solve this other part over here and be finished." When I'd explain "You can't assume it's 90 degrees," or "You're assuming what you're trying to prove," he would grudgingly go along.

So, I think there is a class of math mistakes that come from "a failure to realize that rules in math are not like 'rules' in your everyday life - they are ironclad and irrevocable."