[Cezar]

You did not clearly define 'mistake', then proceed to use a few different meanings in the same paragraph, no wonder your head hurts.

Here is your way out :
Sklansky makes it very clear that the Fundamental Theorem of Poker refers to one very specific type of mistake - playing your hand differently from the way that would've been mathematically correct if you were to know your opponenet's cards.

In the first instance, that's the definition you use - It is incorrect for AJ to call, as if he is to know that you're not bluffing and his ace-high is no good, and assuming no implied odds (are you check-folding the turn if jack hits ?)

Then you perform a back-flip somersault and claim that if you were to check, his bet is not a mistake, because it is +EV against your range of hands. May be so, but you are using a different definition of mistake now. The fact is, here and now, against that Q9 that you have, his bet is a mistake.

Cezar