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.
Corrected entry: 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)
Correction: They bounce back because of the elasticity of the web. That falling block is just a falling piece similar to the long one that is already on the ground, it's not a counter weight.
Correction: I genuinely don't understand this mistake. It's just a piece of debris falling. It looks absolutely nothing like a "counterweight," nor is it big enough to be. It's the exact same color, texture and relative size as the larger pieces of debris on the ground below them. (Furthermore, you can see other, smaller pieces of debris falling around them during the two shots as well.) And the reason they spring back up is because the web is somewhat elastic in quality. This is shown multiple times throughout the movies. He stuck the web to the balcony, and they sprang back up as bits of debris continued to fall. There's no mistake here.
Corrected entry: Several students saw Peter dragging the food tray with his web, but nobody connected it to Spider-Man.
Correction: This assumes the students knew then and there that it was webbing that the tray was attached to and not some other substance. They know Flash bullies Peter and they might have just thought Peter rigged something together to throw the food at Flash in retaliation. We never see any students inspecting the webbing afterwards, so it can't be definitively said that they would be able to connect it to Spider-Man when he emerges months later.
Corrected entry: At the start of the film in the scene with Aunt May and Uncle Ben talking, Uncle Ben picks up a green plate. When he goes to pick it up, there are books, or something, resting by the microwave, which changes position between shots. (00:12:30)
Correction: The books are in the exact same position relative to each other and order in every shot.
Corrected entry: When Peter and his uncle are talking in the car, and the camera is on Peter, you can see lots of plants and bushes in the background. When he gets out of the car, there are no plants or bushes. (00:34:45)
Correction: The main library entrance is flanked by two marble lions and a plaza on its north and south sides. In the shots facing Peter in the car, the camera faces the south library plaza with its "plants/bushes" parallel to the car (note the kiosk topped by a pediment, one of two kiosks that used to be on the north and south plazas). Then, when Peter gets out of the car the plants/bushes haven't actually disappeared, it's just that the angle of the camera is now turned more northward toward the entrance, so we simply can't see the south plaza, though if the camera turned a bit to the left we would see it's still directly across the street from Peter. See street here.
Corrected entry: In the cafeteria Peter web-slings a tray, with hardly any corn on the plate. Then Peter flips it onto Flash and suddenly there's a whole lot of corn on his back. (00:22:55)
Correction: It looks like there's somewhat a layer of corn under the green and orange stuff so on his back the contents are turned upside down. The corn that was hidden below is now over the green and orange stuff.
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.
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.
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.
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.
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: 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.
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.
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.