Audio problem: After Dewey and Miss Mullins go to the bar, Dewey is heard singing and snapping his fingers as he drives. However, you can see through the windshield that both of his hands are on the steering wheel and he is not snapping his fingers.
Audio problem: Right before Dewey walks into the classroom for the first time, he tells the principal, "check." The shot changes to behind Dewey's head and we can see him saying "check" again.
Audio problem: When Dewey starts playing his guitar towards the end (when he was leaning back in his chair with his feet on his desk, then leaned forward and stood up on the desk) we hear the drums starting to play. In the first shot of the class, the drummer is not doing anything except sitting behind the set, and there's still a beat.
Audio problem: In the final battle of the bands scene, when they play Zack's song, you can see a lot of amps on stage but there are only three guitars. There is no need for so many amps with only three guitars and such a small venue. Also if you look closely, the Peavey amp next to the keyboard is the only amp that has a cable connected to it. All the other amps have the guitar input on the front but you can see that none of them are connected to anything, neither are they switched on because you can't see any lights on the front of them.
Answer: The song isn't on the soundtrack, and I can't find anywhere in the film where Jack sings lyrics that even sound like Tears. I don't think it's true.