Factual error: In an early scene, the high school science teacher produces a schematic diagram of the two nuclear bomb designs created by the Manhattan Project. He says, "Here are two designs based on plutonium." Actually, only the Fat Man bomb uses plutonium. The other, the Little Boy design, uses uranium.
Factual error: To achieve critical mass and create a nuclear explosion, the plutonium in Paul's device would have to be compressed very precisely. The sphere he placed it into is too large, when he heats it the plutonium would not be distributed evenly, even if it rotates while heated and the amount of plutonium in the jug he steals is not not nearly enough to fill it completely. A smaller sphere was required.