Continuity mistake: When Peter wakes up the day after he was bitten by the spider and goes to the living room doing a little "stunt", Uncle Ben immediately turns to him, but in the next shot he makes a forward movement as Peter falls on the ground after the stunt.
Continuity mistake: When Peter tries his first web swinging on the rooftop, the sky turns from sunny to cloudy between shots.
Continuity mistake: When Flash is hit by the tray with food he raises his arms in disbelief. A shot later his arms are lowered and he repeats the previous movements.
Continuity mistake: When the movie begins and all the students enter the lab, Mary Jane's boyfriend nags her and she moves her arm to her shoulder, then lowers it. In the following shot her arm is raised and she is lowering it again.
Continuity mistake: When Osborn is getting ready to radiate himself at his laboratory, he throws his clothes on the floor. Their position differs between the first and second shot.
Continuity mistake: The day after Peter gets his powers, while he follows Mary Jane to the school, the sun changes between shots.
Continuity mistake: When Peter is testing the web on the crane, his fringe swaps between messy/ brushed /windy / still between frames in no order whatsoever.
Continuity mistake: When Osborn is drinking whiskey and hears his inner voice, is about to see the African masks and before watching himself in the mirror, his fringe swaps from messy to brushed.
Continuity mistake: When Osborn is laid on the stretcher about to enter the vault, the cables by his right shoulder change positions between shots.
Continuity mistake: When Aunt May opens Peter's sleeve to show his wound, the opening differs between frames.
Continuity mistake: During the famous kiss scene, Mary Jane's hair keeps swapping styles between shots. It changes between hairless cheek then hair on cheek, and soaked and straight to curly hair.
Continuity mistake: When Aunt May is praying, right before being attacked by Goblin, the portrait moves closer/ further away from the quilt between shots.
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