Continuity mistake: This is a little hard to explain. During the Unity Day Festival, after Goblin beats up the cops, the shot cuts and he turns around to face Spider-Man, who lands in front of him. The problem? He was facing the same direction as Spider-Man in the previous shot (you can tell from the background), so it makes no sense that he has to turn around when the camera cuts.
Character mistake: There is a typo on one of the monitors. "human PREformance enhancement" instead of "human PERformance enhancement" (00:16:52)
Revealing mistake: When the car jacker who stole Uncle Ben's car is being chased by the police, they seem to be doing a high speed pursuit. However when the car goes over the corner and demolishes a stand, a cut shows the inside of the car. The digital speedometer is reading 15-17 mph, hardly much of a challenge for the police to catch.
Answer: Remember that Green Goblin (Norman Osborne) just found out that Peter Parker is Spider-Man. Aunt May's comment about everyone knows he loves Mary-Jane concerns him because he now realizes that Green Goblin might find/kidnap Mary-Jane just to lure Spider-Man into a fight. This is the basis for the whole reason he can't be with her, as he would be potentially putting her in harm's way all the time if they got together.
Jazetopher