When Peter meets Mary Jane just after her audition, he tells her "I was in the neighborhood", then goes on to list how many taxis and buses he had to take to get into the neighborhood. This is the exact same line said by Liza Minelli to Dudley Moore in the film "Arthur," at Arthur's engagement party. See more...
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Why would Columbia University have the "most powerful electron microscope on the eastern seaboard" in the same lab room as it would have the spider lab, which is a biology/genetics study? Electron microscopes are useless for studying DNA. The electron beam turns molecules into sludge. All but the toughest organic samples have to be coated with metal as protection, and you can't do this with DNA.
In the graduation scene, watch for the giant spiky orange flowers behind Norman Osborn. These are tropical birds of paradise flowers which grow all over California but would never survive in New York. [Confirmation of that: one contributor was taking a studio tour at Sony studios in Culver City, CA on March 26, 2001, and saw the filming of the graduation scene, complete with Tobey and Kirsten zipping by sitting side-by-side in the jump seat of a golf cart.]
When Spider-Man is hanging under the bridge holding the cable car and the Goblin charges at him the final time, he gets hit on the head by a gas can presumably thrown by one of the motorists watching from the bridge. However, for the can to have hit when and where it did, it would have had to curve out and around a four foot railing and some ten feet of concrete and steel before making its way underneath the bridge and some distance in to strike the Goblin. Not only was this an incredible curve ball that was precisely aimed at a target not directly visible by the person who threw it, but it still managed to impact with enough force to knock the Goblin off course.
During the bridge scene, when the Green Goblin first holds Mary Jane by her throat, his left thumb is visible. All further shots show no thumb under Mary Jane's chin. Actually, the left hand then seems to be holding Mary Jane by her right shoulder. Even when Mary Jane, who is not a super-human, is held by her throat, she is able to move her head, look down and scream.