Every few years I try this. It’s gotten to the point where I can no longer tell if this is actually helpful or illuminating, but below you’ll see the categories that I created when I tried to sort a bunch of mistakes that I’d logged on this site.
Enjoy, and please share any disagreements or alternate sortings that you see in the student work.
Mistakes Due To Limited Applicability of Models
Recursive rather than Relational Thinking
Circular rather than Rectangular Models of Fractions
Non-commutative rather than Commutative Model of Multiplication
Acting Out the Problem rather than Using a More Efficient Strategy
Mistakes Due To Applying Properties of a Familiar Model in an Less Familiar Situation
Linear properties applied in Non-Linear situation
One-Dimensional Distance applied in a Two-Dimensional Situation
Additive properties applied in Multiplicative situation
Side-times-Side Formula for Finding Area Applied in non-Rectangles
Area Properties Applied to Perimeter
Properties of some paradigmatic example of a shape applied globally 
Properties of a Fractional Parts of a Rectangle Applied To Other Shapes
Mistakes Due to Quickly Associating Something In Place Of Another
Squares Instead of Square Roots
Multiplying In Place of Exponentiation
Addition In Place of Multiplication
Changing the Numbers of the Problem
Operating on the “Answer” in an Open Sentence Problem
 This is a very mushed-together category. I’ve fallen into the trap of giving geometry short-shrift in the face of arithmetic and algebra. In general, I understand geometry thinking less well than I understand arithmetic/algebraic thinking. That category of “Properties of Shapes Overextended…” needs some serious breaking-down.