Continuity mistake: When Venom kicks Spiderman's mask off, Spidey's fringe swaps from messy to combed between shots.
Continuity mistake: When Peter surprises MJ in the park, just before he receives the key to the city, MJ says "no, I'm proud of you" at this point they hug, MJ hugs Peter on his left shoulder and when the camera angle changes she's hugged him on his right shoulder.
Continuity mistake: The thickness of the bandage on Harry's forehead differs in length through shots. Use his eyebrows as a reference.
Continuity mistake: At the jazz bar, the waitress left to Gwen keeps appearing and disappearing, and changing positions in less that 10 seconds.
Continuity mistake: In the bell tower, the sweat stain on Eddie's t-shirt increases and decreases all the time.
Continuity mistake: The position of the white debris fallen on the taxi's windshield changes between the first and second shot in less than half a second.
Continuity mistake: When we see Peter riding on his scooter after just visiting Aunt May and telling her he's going to ask MJ to marry him, we can see that Peter is wearing his safety helmet with the strap fastened under his chin, yet when the hobgoblin knocks him off of his scooter and into the air the helmet can be seen flying away like it wasn't even fastened up and secure.
Continuity mistake: Before MJ throws the chunk of concrete at Venom, she has her arms raised holding the chunk in the air. In the close-up of Venom's face MJ can be seen in the background, resting calmly in the cab. Then, when back to a close-up of her, she is holding the chunk as before.
Continuity mistake: After Peter smashes his back against a brick wall, watch the left side close to his ear. The first shot shows several bricks missing. Several seconds later the wall is fixed and there's just a tiny chip missing.
Continuity mistake: When Gwen stares at the steel beam, the beam is perpendicular to the window, pointing in a 7 o'clock direction. A frame later, in a wider angle, it is horizontal to the window.
Continuity mistake: The news reporter is looking upwards and has no camera in front (if she did, a big beam of light would've been on her face). However, when half a second later the angle changes to the news host, the woman is looking down with a camera focusing directly at her.
Continuity mistake: During the very last fight, the bruise on Peter's right cheek keeps increasing and decreasing its redness.
Continuity mistake: During the fight between Harry and Peter at Harry's mansion, just after Peter kicks Harry through the glass window to outside, if you watch closely there is nothing on his right shoulder, then in the following shot a piece of glass appears on his shoulder.
Continuity mistake: Inside the bell tower, when the black slime falls on Eddie he is standing inside the pattern on the floor. In the close-up, 2 frames later, he is standing on the cobblestone outside the pattern.
Continuity mistake: During Venom's 3 second long flight to stab Spidey, moments before he stabs Harry, shots alternate between Spidey and Venom. The stuff behind Spidey keeps changing positions all the time.
Continuity mistake: Inside JK's office, from the back shot the glass of water disappears and the empty mug gets filled with pencils.
Continuity mistake: The blade put against Spidey's throat faces up, then down in less than a second, without Venom moving it.
Continuity mistake: The first time that the crane destroys the office it sweeps desks and furniture, which fall on the people below. However, the second time that the crane strikes, a wide view shows that all of the furniture from the edge remains perfectly placed on the office.
Continuity mistake: JK's cigar when shouting at his secretary disappears from his hand.
Continuity mistake: When Spidey makes Venom explode and watches the metal bars around melted, the one in front is really twisted. Couple seconds later, from another angle, the bar is just sightly bent.
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