Continuity mistake: When Norman is getting ready to test himself, he lies down on the bed, fastens himself in and the doctor goes to the computer. However, when it shows him being brought in to the chamber he has several electrodes connected to his chest and head. (00:15:20)
Visible crew/equipment: When Spider-Man is rescuing Mary Jane from falling to her death from the balcony, he catches her and spins his web to the balcony to save her and they bungie to just inches from the ground. As they are preparing to bounce back up the shot rotates 90 degrees and you can see the counter weight that pulls them back up coming down to the ground. It's a weird one, this - there's a sound effect as the weight comes into view, so it's meant to be there (or else the sound's just a cover), but it can't be anything he attached his web to, as it was stuck straight onto the balcony. If it's falling, they should be too - his web's not pivoting around anything. (01:06:50)
Factual error: Why would Columbia University have the "most powerful electron microscope on the eastern seaboard" in the same lab room as it would have the spider lab, which is a biology/genetics study? Electron microscopes are useless for studying DNA. The electron beam turns molecules into sludge. All but the toughest organic samples have to be coated with metal as protection, and you can't do this with DNA. (00:09:05)
Continuity mistake: When MJ and Peter are discussing the beating that Peter gave Flash that morning in school, MJ says, "He's just glad you didn't give him a black eye for graduation." This scene takes place the day after Peter was bitten by the spider, when the weather is cold. High school graduations generally take place in June or late May - so any black eye Peter might have given Flash would long be healed up by graduation. (00:29:15)
Continuity mistake: During the scene where the apartment building is on fire - a woman points directly up and exclaims, "Look up there!" while Spider-Man is still swinging towards the fire from several blocks away. (01:19:00)
Other mistake: When Spider-Man enters the burning building, the Green Goblin jumps out from under a cloak, punches him in the face and Spider-Man is thrown backwards. However, for Spider-Man to be propelled back the way that he was the Green Goblin would have had to punch him in the torso. Spider-Man's head should have snapped back first when the Green Goblin hit him. (01:23:55)
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.