Factual error: After the turbine trip, Godell says that the reactor water level was "almost up to the steam lines." The fictional Ventana nuclear plant is described as being a pressurized reactor plant and could not possibly have such a problem.
Revealing mistake: When Godell is trying to get away from the company's goons, he races to the nuclear plant gate where he'd be safe. As he pulls up to the gate, you can already see the 'donut' skid marks left in the driveway from the goons' car when it turns around. But the car turns around AFTER Godell pulls up to the gate, so the donut must be from a previous take.
Factual error: When Godell takes over the control room, his colleagues are out in the plant trying to shut it down. In actuality, anyone, especially a trained operator, can do this easily from virtually anywhere in the plant.