Continuity mistake: During the train scene, Spider-Man's mask had gone partially black. We also see it when Spidey puts his mask back on. Yet when Doc brings him to Harry, we don't even see a patch of darkness on his mask.
Visible crew/equipment: On the way to the theater Peter intercepts a police officer chasing a couple of criminals. At the end of that scene one of the police cars has a tremendous wreck that swings the car sideways. There is a clear shot of the driver with a black helmet on.
Continuity mistake: Peter has a small horseshoe-shaped scar on his right cheek. In Dr. Octopus's lab, as Octopus is destroying the fusion reactor, they share a meaningful look and the scar has switched cheeks. (00:26:15 - 01:46:15)
Continuity mistake: When Aunt May hugs Peter near her "hero" speech, she hugs him with her head to his left shoulder. The shot changes and you see that she is now on Peter's right shoulder. The shot changes back and you see her on his left shoulder again.
Revealing mistake: In the scene where Peter saves the child (Venus Lam) from the burning building, right after the jump over the floor opening, the child stands up to help Peter we can see she wears knee pads under her pajamas.
Continuity mistake: In the scene where Peter is riding his scooter to Mary Jane's play, after the music fades out you see a black convertible being chased by several police cars. The black convertible is rammed forcibly, and you see many hideous dents on the side of the car. Thirty seconds later, after Peter is done talking to the kids, we see the same car from the same side it got rammed into, but the hideous dents have vanished. (00:24:25)
Other mistake: At the end, when Peter saves Mary Jane from the collapsing structure, he jumps up in the air and swings her to safety. However if you look at the web he is holding onto it is hanging down vertically. What did he attach the web to that was directly above him, the sky? Every bit of the structure around him was/had collapsed and the only thing remotely close to swing from was the cranes. Yet we see that was quite a distance away, so Peter would have had to shoot the web away from himself not above him. (01:47:50)
Continuity mistake: As Peter stops the elevated train with many webs, a tear appears in his suit on the inside left arm during a closeup. Later, when his arms are still outstreched, there are many shots where you can see that the tear has disappeared; for example, a few shots later when he is still trying to stop the train; when the passengers are lifting him over their heads into the train; and many others.
Continuity mistake: On his last pizza delivery before he gets fired, when it first cuts to the receptionist and the room that she is in, the clock is very high up in this shot, above the receptionist's head, then in the following shot when the receptionist is looking in Peter's direction, the clock is much lower. (00:05:35)
Trivia: Spider-Man creator Stan Lee makes his standard cameo appearance for this film when Spider-Man and Doc Ock are fighting on the side of the building. The first shot of the street during the fight shows a woman being pushed out of the way as some debris falls; the man pushing her is Lee.
Continuity mistake: When Doc Ock escapes from the hospital, he hits a taxi with his tentacle. The taxi goes flying and is about to land on its roof in the middle of the street. The next shot however shows the taxi landing on top of another one, and the taxi is right side up.
Continuity mistake: At the end of the "I've changed" conversation with Mary Jane, the taxi is right next to her as she turns towards it (you can see its roof next to her face), yet in the very next shot she has to cross the street to get to it.
Continuity mistake: Right before Spidey stops the train there's a lot of people inside next to him. Then a wide shot later they've vanished only to reappear a shot later.
Continuity mistake: After Spider-Man stops the train and faints, four hands comfort him. A frame later they've changed positions.
Continuity mistake: When Peter/Spider-Man has his first web failure and falls on the pipes on the building's roof, he keeps his hands free in one shot and then his right hand is put on his chest in the next.
Continuity mistake: Spidey falls on a puddle and takes off his mask, his hair completely messy and wet. A frame later, when he is about to climb a wall, it's neat and brushed.
Visible crew/equipment: After he watches Mary Jane exiting from the theatre with her boyfriend, Peter is running in the alley to put on the costume. On the wet ground you can see the traces of the tires belonging to the camera car used to shoot the scene.
Answer: Unless there is is a deleted scene to shed light on the issue, then it's not really addressed in the movie. It's possible that Doc Ock and Harry had a second meeting that took place off-screen in which Ock revealed to Harry where his hideout was, but as there's nothing really to go on, it's anyone's guess and it's reasonable to consider it a plot hole.
Phaneron ★