Continuity mistake: During the World Unity Festival when the Goblin attacks, there is a shot of Peter tearing off his shirt exposing a costume that is low cut at the neck. However, in the scene when Spider-Man and Mary Jane kiss in the rain, the costume comes halfway up his neck. (01:17:55)
Continuity mistake: When Spider-Man finishes beating up the thugs and after Mary Jane kisses Spider-Man, when you watch the one shot from the side, Mary Jane only starts to put his mask back on. But when the angle changes, Spider-Man's mask is properly on when Mary Jane didn't even move her hands. (01:21:40)
Continuity mistake: In the Thanksgiving dinner scene, watch Mary Jane's arms after Norman asks Peter to repeat how he got hurt. When she is shown close up, her arms are folded. In the long shot, her hands are in her lap. They jump back and forth between the two positions. (01:24:50)
Visible crew/equipment: In the school fight scene where Peter beats Flash by punching him and making him collide against a teacher, his tray falls on his face. In that precise moment a camera with a hand on it can be briefly seen on the left side of the screen just a few moments before the shot points downwards.
Continuity mistake: When Mary Jane falls off the balcony she falls sideways except for a shot of her falling face down. Shot changes and she is falling sideways again.
Continuity mistake: When Flash is hit by the tray with food he raises his arms in disbelief. A shot later his arms are lowered and he repeats the previous movements.
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: When Peter wakes up the day after he was bitten by the spider and goes to the living room doing a little "stunt", Uncle Ben immediately turns to him, but in the next shot he makes a forward movement as Peter falls on the ground after the stunt.
Continuity mistake: When Peter tries his first web swinging on the rooftop, the sky turns from sunny to cloudy between shots.