In the scene with Jim super-gluing himself to himself and just after the police tell him to 'freeze', if you listen closely you can hear the radio say 'Right George K' which, if you listen hard enough, is said all the time the police are chasing you on all the Grand Theft Auto games. See more...
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Continuity: In the scene where the Asian guy is taking a piss of the balcony at Stifler's party, you see Stifler and his girl stand up when the pee hits the pillow. Then the camera is switched to the balcony where the Asian guy and a girl are talking. Then again we see Stifler and his girlfriend, but now the pillow is dry again.
Deliberate "mistake": During the "breaking up" scene with Jim and Michelle when they're inside the cabin, her hair is crimpy, but when she walks outside and gets into her car, her hair is straight. This is because Alyson Hannigan filmed this particular scene during a break in the filming of a "Buffy the Vampire Slayer" episode.
Continuity: When Jim is sitting with his Dad in the waiting room, after he glued himself, he is holding the videotape at an angle which is toward him. The woman in the wheelchair could not possibly see the title of the video but, when they show her noticing it, the tape is being held at an angle facing towards her.