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.
Visible crew/equipment: In the very last scene of Mary Jane looking over the city in Peter's apartment, there is a reflection in the window where the camera lens and cameraman are partially visible.
Continuity mistake: Regarding the scene where Doc Ock has delivered Spider-Man to Harry's mansion, when Harry pulls off Spider-Man's mask, there is a very obvious and bad splice. The "mask on" Spidey's head is in a different position and further away than the "mask off" Spidey's head.
Continuity mistake: During the final conversation between Spider-Man and Doc Ock, the rips in Spider-Man's suit keep changing. For instance, there is a tear on his right shoulder; for most of the scene, there is a single piece of black webbing left holding the rip together, but when Doc Ock grabs Spider-Man's arm, the rip now has two pieces of black webbing. Then it goes back to one.
Plot hole: Dr Octo builds a new, bigger machine and it starts to pull the building in on itself, but it's so strong it also manages to pull all the metal from the streets as well, including cars. When Spiderman saves MJ, the metal cranes have somehow managed not to be pulled in or at least bent by this massive machine that made a building collapse on itself.
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: In the scene with Peter's "I'm back!" jump, It shows a shot from above and you can see his solid outlined shadow in front of him. However, in the very next shot it shows you a close up of Peter walking, and there is no longer a shadow there.
Continuity mistake: When Peter visits the doctor, look closely at the skeleton behind him. In the first shot, you can see two spots of light reflected on its skull; in subsequent shots, there is only one spot of light.
Other mistake: When Spider-Man shoots a single web out of each arm to stop the train, in the shots of his reactions, you can see that he is holding many webs in each hand. Then when he shoots multiple webs to try and stop the train, he has the same amount of different webs as before. Obviously they didn't have footage of him just holding a single web, and used shots from later in the sequence.
Revealing mistake: As Mary-Jane is being lowered onto the crane after Spidey has saved her, you can see that her dress is being held together to stop the split up her leg opening up too much. However in the next shot when she runs down the steps towards her fiance, the dress is flapping around and the split is wide open.
Continuity mistake: When Doc Ock carried MJ up the side of the building after he kidnapped her, one of the D'Agostino banners was ripped out of the building and fell. But when Peter came out of the deli and looked across the street, the banner was back on the building and the building wall showed no sign of damage from Doc Ock's tentacles.
Revealing mistake: When Doc Ock comes out of the hospital and throws a car onto another one, you can tell that the man in there is just a dummy. He has no reaction whatsoever. He just sits there as if nothing happened.
Continuity mistake: There are two close-ups of Peter's head when he is lying on the floor of the train: one of the shots has a black shoe with white laces very near his head, the other a blue, white, and black shoe, also right next to his head. In the wider overhead shots of Peter, no one standing around him is wearing shoes like that, nor are they standing close enough for their feet to be in the close-up shot in the first place.
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: After Doc Ock throws the car through the side of the deli, it shows Peter and MJ from outside the building and there's a table with a chair at the base of the hole right up next to the nonexistent wall. For the rest of the scene, the table and chair are not there.
Other mistake: When Peter Parker is walking down the streets of NYC on his first day as a "normal, powerless human" It is clear that the people in the background are not extras. You can see several people watching him during the shooting of the scenes.
Revealing mistake: In the scene where Spider-Man is pushed inside the train by Dr. Octopus and grabs the bar then leaps to the next: The passengers are all looking where they've been told Spider-Man is supposed to be, but none of them are actually looking at him, revealing that he is a CGI image and not an actor.
Factual error: When Spider-Man is fighting with Doc Ock and Doc Ock throws Spider-Man through the overhead pedestrian bridge, Doc Ock throws Spider-man in the direction of travel of the train, and when passing through the bridge, Spider-Man doesn't touch anything. When Spider-Man comes out the other side, he is "behind" Doc Ock (in terms of the direction of train travel). This implies that Spider-Man has slowed down in the air - fair enough due to wind resistance - and so is traveling slower. However, Spider-Man then hits Doc Ock from behind, meaning he's now sped himself up in mid air. He doesn't use any webs.
Other mistake: Sure Spider-Man has super human powers, but his costume doesn't (as we see as it rips and tears quite a lot through the movie) so how come the back of it is still intact and not even dirty after being dragged over the street by a train that's going at high speed?
Other mistake: When Spider-Man and Mary Jane are sweet-talking in the web, her hair blows around freely, whereas considering how sticky a spider web is, her hair should be sticking fast to it. Permanently. After all, the web cannot be sticky enough to hold her body, while not being sticky enough to glue her hair.
Answer: While it's never mentioned in the film, the most likely explanation is that Harry, as a rich kid, grew tired of "slumming it" and decided to move back into his mansion.