Stupidity: Early in the film, Peter Parker desperately wants to see Mary Jane's performance, but he is turned away at the theatre doors because he is a few minutes late. Defeated, Peter shuffles away and sulks. Seriously? Why couldn't Peter simply enter the theatre through a side door or the roof? He's Spider Man.
Suggested correction: There's two things to consider here. First, a major theme of the film is Peter struggling with keeping his Spider-Man and Peter Parker lives separate. Peter makes every attempt to get to the show on his own, as Peter by riding on his scooter. Simply breaking into the theater after he has been turned away would ruin the idea that keeping his two lives separate is a struggle. It would instead imply the opposite, that Peter can simply use his powers to solve his problems whenever it's convenient. Secondly, the usher makes it clear that no-one is to be admitted after the show has started as this would disturb the guests and possibly the performers as well. Sneaking into the theater could very well ruin the performance and Peter obviously wouldn't want that.
If there's one thing we know about Spider-Man, it's that he is incredibly stealthy, often coming and going without any detection whatsoever. He could have easily accessed the building and watched the show from a secluded vantage and even met Mary Jane backstage afterwards. Certainly in this case, using his powers would be justified, given that it was more important for Mary Jane to know Peter attended the show, rather than simply giving up.
He doesn't want to do any of that, though. He wants to go to the show as Peter, with a ticket, sit in a seat with the rest of the people, enjoy the show, and see Mary Jane afterwards. He stops the car chase as Spider-Man after his scooter is wrecked and instead of web-swinging to the theater, which would have been much faster, he chooses to change back into his regular clothes and drive the criminal's car. Sure, he certainly could have used his powers to get into the theater but the point is he doesn't want to. The fact that he chooses not to use his powers and instead deal with the consequences of hurting Mary Jane's feelings is the entire point.
And besides he'd probably get kicked out of the theater if he was caught.
