I'm guessing you're talking about Betty when you say he slept with a married woman? Was that ever explicitly said or just hinted at?
In that instance, if they did sleep together, I'm not sure you can call it giving in to his more base instincts. She's someone he cares about, asking him for emotional reassurance. If the two people involve have a romantic history, that situation can easily turn sexual even if the person trying to do the comforting really is trying to do the best thing for the other person. That isn't to say it really is the best thing to do. In fact, if that's what Peter did, it was pretty stupid, but it could easily have seen like the best thing to do at the time.
Is it a moral failing? Maybe, but what's the moral imperative here. To never sleep with a married woman, no matter what? To do whatever it takes to comfort a friend? To try to preserve Betty and Ned's marriage?
If I were going to name a moral failure, I would use the scene in ASM 122, where he decides to go after the Green Goblin instead of helping Harry, which was definitely giving into a base instinct, though it would have taken superhuman effort not to, given the situation and, to his credit, he recognized it as a moral failure at the time.