Plot hole: Harry tells Doc Ock that in order to find Spider-Man he must find Peter first. Doc Ock finds Peter with Mary Jane in the cafe and throws a car through the window straight at them, then later throws Peter against a brick wall. Any normal person would've been killed instantly (or very badly injured), and Doc Ock doesn't yet know that Peter is Spider-Man. Given that Peter is his only lead on Spider-Man, it makes no sense that Doc Ock would try to kill him.
Factual error: Dr. Octavius says his fusion relies on tritium and that there is only 25 pounds of the substance in the world. In reality, tritium is a good deal more common than that. From this article (http://www.epa.gov/radiation/radionuclides/tritium.htm): "It is used in various self-luminescent devices, such as exit signs in buildings, aircraft dials, gauges, luminous paints, and wristwatches. Tritium is also used in life science research, and in studies investigating the safety of potential new drugs." There's also a large region of water near Antarctica which is rich in tritium.
Other mistake: The Spider-Man outfit that Peter throws in the trash appears to either have the head attached to the body or a very long neck on the mask. It hangs too far down over the edge of trash can to be the same, separate headpiece, with a short neck, that Jameson receives from the trash collector. (Though this may be a deliberate nod to the comic book, it is still a mistake.)
Stupidity: Early in the film, Peter Parker desperately wants to see Mary Jane's performance, but he is turned away at the theatre doors because he is a few minutes late. Defeated, Peter shuffles away and sulks. Seriously? Why couldn't Peter simply enter the theatre through a side door or the roof? He's Spider Man.