Factual error: During the fight scene with Sandman in the armored car, the Terminal Tower can be seen in the background, which is a landmark in Cleveland, Ohio (where the scene was shot), not in New York City.
Continuity mistake: During Sandman's attempted heist of the armored truck, he punches Spider-Man through the side of the truck, and the damage to the armored wall significantly changes in the following shots.
Continuity mistake: Down in the sewer, the wad of dollar bills moves away from the puddle between the close and wide angles.
Trivia: Stan Lee, the creator of Spider-Man, makes a cameo appearance when Peter Parker is reading about Spider-Man getting the key to the city. He is the man that walks up and talks to him.
Continuity mistake: When Peter lands on the cab, MJ has her fringe all messed up and says "Peter, we'll both die". angle on Spidey, and when back to MJ she's perfectly combed and neat looking.
Continuity mistake: When Peter first goes to see Aunt May and tells her he's going to ask her to marry him, Aunt May in the first shot goes to hug Peter on his left shoulder, it cuts away and in the following shot she has hugged Peter on his right shoulder so that the camera can see Peter's face.
Continuity mistake: When the office floor collapses, Gwen and a girl in green are struggling not to fall down. In a close-up, one second later, the girl is replaced by a chair. She can be seen several meters away, next to a guy who magically appeared on scene.
Continuity mistake: When Peter is thrown against a brick wall, he produces a big hole around his left shoulder. In the close-up the hole is smaller.
Continuity mistake: Before the cop climbs on the truck, he shields himself on the truck's cabin and you can easily notice the tarp is perfectly tied by a dozen strings. When he climbs up, all the knots magically untie and he manages to pull the tarp away. His buddy couldn't have done it because he always appears with the gun in his hand, covering him.
Continuity mistake: The Bank truck full stops away from a zebra crossing, but the close shot shows it on top of it.
Continuity mistake: The first close shot of Harry in bed shows his pyjama opened with a nipple showing. Half a second later, the pyjama appears closed and the nipple covered.
Continuity mistake: Before Sandman falls down to the sewer, he lets go a bunch of dollar wads. When he is free falling the money disappears.
Revealing mistake: When Spidey is placing the tubes around Venom, his face is obvious CGI except for some shots of him shouting. Here, a real face (twice as big as it should) has been pasted on the CGI body, looking quite ridiculous.
Continuity mistake: When Gwen is sliding down the office floor, she is facing upwards. Half a second later she is facing downwards.
Continuity mistake: The blade put against Spidey's throat faces up, then down in less than a second, without Venom moving it.
Continuity mistake: When Spidey lands on the hanging cab the red LEDs of the meter are glowing. Seconds later, when the roof is blown away, the meter disappears (either blown out or disconnected), but reappears glowing half a second later.
Continuity mistake: In JK's office, the first three bottles of pills are equidistant from each other. From the back, two of them are very close together.
Continuity mistake: When the sacks of money are handed over to the guard at the back of the armored truck, note the license plate number begins with "13022" but then it changes to "48321" during the rest of the scene. (00:49:20)
Revealing mistake: After Peter knocked out Harry/New Goblin and tried a cardiac massage on him, you can see his foot accidentally moving a fake black painted length of cloth put under Harry's body to simulate the asphalt and not let the actor get dirty. (00:21:45)
Revealing mistake: When Peter and Harry are fighting into the Goblin's lair, stunt cables are visible on their backs holding them.
Chosen answer: Answered in the comics: Peter's Spider-Sense tells him if someone is looking when he's about to enter/exit the apartment as Spider-Man.
Captain Defenestrator