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 Osborn'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 says some lizards can regrow lost limbs "at will". The regrowth is an automatic process like hair growth on mammals, no "will" is involved. He is imputing will to a natural process, a rather clumsy anthropomorphic metaphor for someone who should know much better.
When the police SWAT team are seen approaching Spider-Man after he had been downed by the stun dart, one of the officers is looking through the scope of his automatic rifle with the flip cover closed, meaning he wouldn't be able to see through the scope.
At the climax of the film, the countdown for the launch of the projectile begins with "Launch in T minus 3 minutes"
"T minus ..." indicates something is going to happen in a set time. The announcement should have either said "Countdown at T minus 3" or "Launching in 3 minutes".
When Lizard finds 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 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.
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.
The first time that Peter attacks a guy in the city, while he is being chased the men climb to the roof much too quickly; by the time Peter gets to the top they are arriving at the roof. In reality, it would take much longer to climb those staircases.
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.
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'.
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.
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.
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.
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.
At the fight scene in the end, Peter had cuts on his nose and left corner of his mouth (among others on his face). When he got home to Aunt May, those cuts were no longer visible but the others were still there.
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 Hills, Queens, NY. The Q-train did travel to Queens at the time of filming, but it went to Astoria at the north-western tip of the borough. The correct trains for Peter to be on would be the R M F or E.
Additionally, the Q ran above ground in most of Brooklyn, including the approach to Coney Island.
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.
Towards the end of the movie Gwen Stacy sets off the fire control system and hides in the Oscorp lab, causing the fire doors to shut and fire fighting agent to be released. The agent was either; CO2, and would fight fires by displacing all of the oxygen in the room resulting in an asphyxiated Gwen, or Halon (commonly used in industrial settings) that can cause nerve damage when in high enough concentration and with prolonged exposure as well as asphyxiation.
After Dr. Connors injects himself with the serum for the first time, the effects of the transformation kick in very quickly. However, when it is tested on Freddie, the serum takes a very long time to take effect. This is also supported by the fact that a rat has less blood than a human, meaning that the transformation should have occurred almost instantly.
After Uncle Ben was killed by a robber who shot him with a gun. The police comes to Peter Parker's house and gives him the description of the killer revealing that he had a tattoo on his arm. Later on in the movie, the killer was quickly forgotten as Dr. Conner was wrecking havoc in New York City. The killer was never sought out and it's unknown if Peter Parker will ever find the killer that killed Uncle Ben or even bring him to justice as it was never filmed in the first movie and even in the sequel "The Amazing Spider-Man 2" which never had Peter Parker looking for the killer who killed Uncle Ben.
Dr. Connors' right arm-stump is very muscular. However, as anyone who has worked with amputees knows, after several years of having an amputated limb, the remaining stump still attached, experiences degeneration and is withered.
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.
When Spider-Man is making his way to Oscorp to stop the Lizard, Stacey's men attempt shoot electric shock darts at him. One dart 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.
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.
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 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.
Gwen is walking away from Peter so he shoots a web at her, and she turns to face him. He then tugs on the silk, spinning her round to come much closer - when in fact this action should rotate Gwen the other way, and then pull her backwards.
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.