Towards the end of the film, Gwen leaves the Oscorp tower to meet Captain Stacy at the sidewalk. We hear the sound effect of his car screeching to a stop, but the car is already stopped with the door open from the start of the scene.
When Dr. Connors is talking to Norman Osbourne's representative, and when Capt. Stacy is talking to Peter in the station, we see shots of both these characters from the side. Their lips do not match up with the audio.
When Dr. Connors is talking about the ability of some lizards to regrow limbs he says they can regrow limbs "at will". The regrowth of limbs is an automatic process, no "will" is involved. The imputation of will to natural processes is a common error.
When Spider-Man is making his way to Oscorp to stop the Lizard, NYPD attempts to stop Spider-Man by firing electric shock darts at him. One of the darts pierces his torso and stuns him. It's shown still attached as he falls. However, once he hits the ground, the dart disappears without him (or anyone else) removing it. He even receives a second mild shock from the missing dart as he lays face-down on the ground.
While Peter and his Uncle are talking, Uncle Ben plays with a Rubik's Cube. He then places it on the corner of Peter's desk when leaving; however in the next shot the cube jumps to the other side of the desk next to the Peter's computer.
When Dr. Connors becomes the lizard, he becomes far more massive than his human state, shredding his clothes - logically, this should leave him naked. Yet after his first transformation, he is seen in the sewer with a towel/robe on his body.
Earlier in Richard Parker's file the Decay Rate Algorithm ends with a term of 'alpha' (a Greek letter used as a variable) times 't'. Later when Peter writes it for Dr. Connors, he replaces 'alpha' with an 'x'.
When Peter first talks to Gwen in the school corridor, he pulls both earphones out of his ears but then his right ear clearly has an ear bud and wire dangling from it throughout the rest of the conversation.
Captain Stacey leaves the high school in an helicopter with a surveillance camera attached to its belly. When the helicopter is flying over Manhattan the camera, which should be visible hanging close to the tail of the helicopter, is missing.
When Lizard finds Peter/Spider-man in the sewer on his web (when trying to get pictures of Lizard), Lizard scratches Peter from the top of his chest down. In the next scene where Peter shows up at Gwen's window, his cuts go from the top of his left shoulder diagonally down to the right side.
When Peter is examining the contents of his father's briefcase on the floor, among the items there is a quarter. After Uncle Ben comes to the door and Peter is clearing the items away, there is now a quarter and a penny.
When Peter and Flash have their showdown in the school hall, Peter hands his camera to the girl painting the banner. When he does, the camera strap gets loose and hangs from her hand. In the next shot the strap is instead tucked in her hand.
After Peter falls into the wrestling ring after being chased there is a piece of wood which embeds itself upright in the floor. In the shot where it pans out to show him looking at the picture on the wall the wood is no longer upright and some others have changed positions.
While The Lizard is attacking the bridge, Dr. Rajit Ratha's car is bumped and pushed diagonally to the side by another car. However, in the next shot from the inside of the car, it's clear that all of the cars are in a straight row, as if nothing had happened.
After Peter saves a student from Flash's bullying, Peter sits in his chair in the classroom and puts his head down, resting it on his camera. The immediate next shot from the back of his head shows him sitting upright, putting his head down again.
When Peter first discovers his powers on the train (Q-train), it was leaving Manhattan (Oscorp Tower) heading towards Coney Island, Brooklyn (last stop). Peter Parker lives in Forest Hill, Queens, NY. The Q-train only runs through the boroughs of Manhattan and Brooklyn.
In an establishing shot of the location of the Oscorp tower, when Peter first visits, it is actually the Hearst building located on the southwest corner of 8th and 57th. Then in a later aerial establishing shot they show it to be behind Grand Central Station, some 20 blocks away in the current location of the MetLife building.
While a Police Chief, Captain or Commissioner can issue an order to arrest someone wanted for questioning, they cannot issue an arrest warrant as Captain Stacy did. Only a judge can issue an arrest warrant.
Dr. Connors' remaining right arm is seen to be pretty muscular. However, as anyone who has worked with amputees knows, after several years of having an amputated limb, the part of the limb that is still attached, experiences degeneration and is withered.
During the race to the tower, just before the crane sequence we can see Spider-Man falling violently onto a fire escape (at around 1h 45 mins). It is clearly made of rubber and can be seen bending and vibrating.
When Peter is taking a picture of Gwen, there is a point of view shot of Peter's rangefinder camera that shows the viewfinder markings not consistent with rangefinder cameras. It shows instead an SLR camera's viewfinder markings, something people are more familiar with.
The goof items below may give away important plot points.
When Gwen Stacy visits Peter Parker's house at the end of the movie, Peter stands on the porch in front of the glass door. Behind the glass it is dark suggesting that the light is off. However, when Peter re-enters numerous lights are on inside the front hallway.
After the funeral when Gwen and Peter are talking on his front porch you can see behind him that his house number - 36 - is cleanly painted on the door with a black outline. After Gwen leaves and Peter shuts the door the number is then painted on very messily.
When Peter breaks up with Gwen and she leaves, he is momentarily shown standing behind the glass front door. From this angle, the house number 36 that is painted on the glass is shown to be somewhat weathered, chipped/faded. However, earlier in the film, Peter accidentally shattered the door storming out of the house after fighting with his aunt and uncle. Since the glass was clearly replaced, the number would have been very recently painted on it, so the paint should look much newer.
Near the end of the film when Gwen is holding the umbrella in the rain, she moves it to look up and not a drop of rain gets on her face. Once done looking, she puts umbrella back up to have it drenched in the pouring rain.