Continuity mistake: In Spider-Man 2, Otto Octavius knows Dr Connors and is friends with him. In this film, when meeting the Dr Connors from The Amazing Spider-Man, he claims to have never heard the name before.
Suggested correction: He knows the Curt Connors from Spider-Man 2. The Curt Connors from Spider-Man 2 is not the same one from The Amazing Spider-Man, since they were played by two completely different actors. This can't be a continuity error since he's not from the same universe as the Dr Connors from The Amazing Spider-Man.
Continuity mistake: Doc Ock is supposedly from Spider-Man 2 yet here he's gained a sweatshirt or turtleneck whereas in that movie he didn't have one. It's made clear he was pulled from his timeline just before his death, so he should be wearing the same thing.
Suggested correction: I mean how much time took place between the spell casting and his arrival at the bridge? I'm sure there was some confusion.
Continuity mistake: In addition to the sweatshirt or turtleneck, Ock's wearing the pair of sunglasses he wore for the bank robbery. Impossible as those were broken by Aunt May. He should've had on the other pair he wore late in the movie.
Suggested correction: When you think about it, the Doc Ock that shows up both knows who Spider-Man is and is still being controlled by the tentacles. In Spiderman 2 this happens minutes before his death, when he convinces the tentacles to listen to him now. So, he had to have been pulled out during his exchange with Spiderman, which seems highly unlikely. Or, this is an even different Doc Ock that still has that pair of sunglasses and probably found out who Spider-Man was at a different point in time.
Continuity mistake: The green lights on the arc-reactor-looking device that Peter uses to extract electricity from Max Dillon (Electro) light up in a counterclockwise direction. Later, in a close-up shot when Norman Osborne (Green Goblin) is speaking, the lights are lighting up in a clockwise direction.