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)
Suggested correction: At first the electrodes are beside Norman's head. While the doctor is fixing him in place, at one point camera focuses on his face. Later when he's stepping back for the PC, the electrodes can actually be seen stuck on his body. You can see them if you have an HD copy. So the camera focusing on his face is indicating that the doctor's doing whatever necessary for the process.
Trivia: When Peter first brings pictures to the Bugle and asks JJJ for a job JJJ says he'll send Peter Christmas meat. Inside joke because Tobey Maguire is a strict vegetarian.
Suggested correction: Without a source confirming that it seems more likely that it's a simple joke demonstrating JJs lack of generosity, tact and thoughtfulness.
This information is also available on the trivia track on the DVD and Blu-Ray.
The website IMDB and Wikipedia both confirm this.
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)
Suggested correction: DNA labeled with heavy atoms can be seen in electron microscopes. While DNA sequencing isn't yet viable with electron microscopes, transmission electron microscopy DNA sequencing could be possible. Given the fictitious advancements in science seen in Spider-Man, it's possible they can successfully sequence DNA as well.
Trivia: When the board has fired Norman, the board member in the wheelchair is wearing a dark tie with thin colored stripes on it. Later on Peter is wearing this exact tie at Thanksgiving dinner. (01:23:35)
Suggested correction: They look similar, but it's not the exact tie. The stripes are going in the opposite direction, and it's a different color. Peter's tie looks like the one he was wearing at graduation.
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)
Suggested correction: I think it's just figurative speech, exaggeration. He hits him on the chest after all.
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)
Suggested correction: Movie scenes are not always in exact chronological order. A powerful attack getting shown 3 times from different angles for dramatic effect does not mean it happened 3 times. When woman points up, the movie shows Spider-Man approaching starting from a few seconds prior in time to show us some cool swinging action.
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)
Suggested correction: He hits the face so naturally his head is flying and the body is following.
Continuity mistake: Bone Saw had four valets during the wrestling scene yet during the cage match he's only got three at ringside, one of the two blondes disappears.
Suggested correction: I just loaded up the scene. All four of them are definitely there during the cage match. There's even several shots where you can see all four at the same time.
Continuity mistake: When Spider-Man is being gassed by the Green Goblin, the mouthpiece of the Green Goblin's mask is open, and Osborne's lips are visible moving as he speaks to J. Jonah Jameson. Later in the scene where Spider-Man fights the Green Goblin in the burning building, a close-up of his mask is shown again, but this time there appears to be some kind of black mesh screen in the mouth of his mask.
Suggested correction: It's never fully open, it's just easier to see through the mesh in certain lighting.
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.
Suggested correction: I think it's the green smoke reflecting on his glasses. The chamber has rectangular windows so that's why the reflections are rectangular.
I don't think it's green screen, they look a bit small for that but there's something there, you are right. There're green little rectangles on his glasses even when he is doing CPR, when he is looking directly at Norman's face but no green stuff around Norman's head. Perhaps green smoke would be harmful or expensive, so they used regular white vapor and shone green lights on the smoke to make it appear green and later forgot to turn those lights off.
There are monitors with green colored animations throughout that scene, in fact we can see a monitor behind the doctor in the shared screenshot. It could be that the monitor is getting reflected on the glass walls of the chamber which then gets reflected on doctor's glasses.