I think they got some of the physics wrong, but not in plot-critical ways.
Really minor spoiler that you already saw in the commercials:
I thought it was impossible for a reactor coolant failure to result in a bomb-like detonation? I thought that kind of slowly-ramping-up chain reaction would just get you a small sun that would then melt through the floor and head core-ward? They were also worried about the warheads detonating, which I thought was similarly impossible to do by accident. You can get a big toxic mess, but not an explosion.