Revealing mistake: When Norman awakes and throws his assistant into the equipment, you can see it is the assistant's stuntman, as when he is thrown, he has black hair, and the real assistant has brownish-grayish hair. (00:17:40)
Revealing mistake: When Peter catches MJ's falling lunch, the apple lands on its side and doesn't move at all, despite it being round and the tray being moved about so abruptly. Blatantly glued down. (00:22:10)
Revealing mistake: Flash attacks Peter in the school's hallway. We are supposed to witness Peter's incredible speed in one shot, as he dodges a punch in slow motion. Flash's bracelet, however, is motionless. The speed of the punch would throw it back and forth, as it does throughout the rest of the scene. (00:23:50)
Revealing mistake: When Peter Parker first discovers he can climb up walls (while in citizen clothing), he tests it out by climbing up a building in an alley. During this scene, you can clearly see his clothes hanging out forwards, indicating that the scene was filmed with him crawling along a floor horizontally. (00:24:50)
Revealing mistake: Peter Parker climbs his first wall in an alleyway. Look carefully at his shadow - it is directly in front of him on the wall the whole time, indicating that he is being lit from directly behind. The only thing behind him is the opposite wall. The only possible light sources would be from the opening of the alleyway (which would have cast a long shadow to his left) or from above (which would have cast a long shadow behind him). (00:24:50)
Revealing mistake: When Peter is jumping from building to building after he first learns he has powers, you can see that he is jumping over the same alley over and over, only taken at different angles. The clotheslines (and the shadow of them on the wall) is a good pointer. (00:25:10)
Revealing mistake: When the Green Goblin attacks J. Jonah Jameson at the office, Spider-Man shows up. Goblin turns his glider to face his nemesis. If you look closely, you can tell that it is a rotating rig, and that the film was sped up. Goblin's body shifts abruptly while he turns, and the fire in the background is moving too quickly to be at normal speed. (01:15:20)
Revealing mistake: During the final fight with the Goblin, Spider-Man is up against the wall and the Goblin goes to stab him with his "quad bladed knife". Spider-Man grabs 2 of the blades and while pushing back you can see all 4 ends of the blades vibrating up and down as if they were made out of rubber. (01:46:55)
Revealing mistake: At the end of the movie, when Peter is placing Dr. Osborn on the couch after he died, as Peter is lowering him, Dr. Osborn's hand changes from being stiff to the hand moving to help being put down. While it's possible it was a natural reflex, I don't think that they are able to help lower themselves with their own hand. Dr. Osborn had been dead for a while anyway. (01:49:50)
Revealing mistake: When Norman's assistant is securing his head in place in the machine, you can see a reflection of the green screens in his glasses.
Revealing mistake: When the car jacker who stole Uncle Ben's car is being chased by the police, they seem to be doing a high speed pursuit. However when the car goes over the corner and demolishes a stand, a cut shows the inside of the car. The digital speedometer is reading 15-17 mph, hardly much of a challenge for the police to catch.
Revealing mistake: When Osborn is gassed inside the vault and the doctor comes to aid him, 2 green squares are reflected on his glasses. The green fumes are already gone so it can't be that. Plus from the opposite angle there's no green wall anywhere, so it was the green screen used on the set or a continuity error when fumes were still on the set.