Continuity mistake: When Peter stops his motorbike by a grocery store, a group of children suddenly appear out of nowhere.
Continuity mistake: When Octopus's house is about to fall on Mary Jane, the box to her left swaps to being on the right side in the front angles.
Continuity mistake: Mary Jane runs in her wedding dress by a fountain in an empty park. A frame later it's packed with people.
Continuity mistake: When Peter and MJ are in the cafe, before Doc Ock attacks, the same sequence of cars and pedestrians outside the window goes by several times. Pay particular attention when the taxi goes by.
Revealing mistake: After Tobey Maguire stops the train, he is stopped from falling by the passengers on the train. As he pulled back into the train, the vertical metal hand rail on the left-hand side bends and shakes like jelly when it is gently touched by the male passenger as he pushes Tobey into the train even though the hand rail is still intact and fixed to the train. This is probably used so Tobey would not be injured while pressing up against the train during the filming of the scene.
Revealing mistake: When Peter returns to his old life and walks on the notes of "Raindrops Keep Fallin' on My Head", at a certain point he stumbles and behind him some people look at the camera.
Suggested correction: They are looking in the direction of the camera. It doesn't necessarily mean they are looking at the camera. They could just as well be looking at Peter since he stumbled and fell, which is a pretty normal thing for people to do when someone falls down.
Actually people behind him keeps watching even when Peter restarts to walk normally. I think if they were really watching just him, they would have looked away immediately as he got to his feet.
Continuity mistake: During the demonstration of the fusion reaction when Doc Ock is strapping the metal arms to his body, the pins that go in to his spine are shown going in twice from two different angles.
Continuity mistake: In the scene where Peter and Aunt May visit Uncle Ben's grave, Peter's hair is blowing in the wind quite violently in the wide shot but is relatively still in the close up.
Continuity mistake: During the train fight, Spider-Man is about to be run over by a passing train, and he leans against the windows to avoid it. From the front angle his body is leaning on two separate windows, but from the angle inside it's leaning on a single one.
Continuity mistake: Dr. Ock is showing his tentacles and says "Let the show begin" and walks by a round platform on his left. When the angle changes he is behind the platform and is walking past it again.
Continuity mistake: Mr. Ditkovich takes a 20$ bill from Peter and his daughter throws a spoon on the burning stove. A frame later the spoon has turned 180ยบ around.
Continuity mistake: Dr. Ock's machine creates a tritium ball, and projects several light beams towards it. Just a frame later, in the close-up, the pattern of the beams is completely different.
Continuity mistake: After knowing that Mary Jane is to be married, Spider-Man falls on a puddle, but no water drips from his suit. Seconds later, he falls again and now water does drip.
Continuity mistake: As you are listening to the bank guard tell Doctor Octopus, "Put your arms up! All of them!", look at the money cart inside the vault. It goes from just a few items on it at first, to having a multitude of items on it, as well as around it, in later shots of the scene. (00:48:15 - 00:49:05)