Off the top of my head, for those that are curious:
The show depicts radiation as similar to a contagion. In real life, once you strip and wash someone exposed to radioactive contaminants, they pose no danger to others.
The reactor was never in danger of turning into a nuke or rendering huge swathes of Europe uninhabitable. Nuclear explosions only happen under tightly engineered conditions. A big pile of molten reactor slag, while certainly dangerous, can’t turn into a bomb.
However, the utter incompetence of the USSR is very accurate.