Factual error: Considering the brightness of the fusion process, Dr. Octavius has to wear special goggles to be able to see it. Yet no one else in the room is wearing such goggles or seem hurt by watching the whole process, just as at the end of the movie. When welding something, no one can look at the arc that's created, as it would hurt his eyes and burn his retina; presumably, the fusion process would be brighter and more powerful than that, and so should have some kind of damaging effect on everyone's eyesight (except Spider Man's, maybe).
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.
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.
Factual error: In the scene where Peter is saving the children from the burning building, there is no smoke from the fire, when there should be black smoke billowing out the windows. He wouldn't be able to just stand up and walk through the building. But in order for the scene to play out on camera, the area is smoke free. A fire in an apartment or office building will include combusting of large amounts of plastics (computers and so on). So unless there is nothing but alcohols in the building there will be immense amounts of smoke.
Factual error: The only elevated trains in Manhattan are Metro North that goes to Connecticut and the N, Q, R, W line that goes to Brooklyn/Queens, and that line goes over a bridge. None of these trains are elevated in mid-Manhattan; and most certainly, the end of the subway line would not just be a big metal "bumper" that leads into the water.
Factual error: Harry stumbles onto his dad's secret room and it is free of dust except for a few cobwebs. While there may have been no human activity in the room for almost two years, there were holes in the room that let sunlight, air, and insects/arachnids in, therefore there must have been airflow. With the airflow, dust or dirt should have entered the room and collected on the items.