Other mistake: The reactor at Chernobyl exploded at 1:23 AM. Near the beginning of the episode, we can see that Vasily Ignatenko was at home with his wife, sleeping in his underwear, when they were both startled by the explosion. Later on, we see him in full gear, entering the power plant on a fire truck. We're informed on-screen that it's 1:30 AM. That means that Vasily had to get dressed, get to the fire station, put on his gear, get in the fire truck and get to the plant (~3 km away) in 7 minutes. Impossible. In fact, the first firefighters arrived at Chernobyl at 1:45 AM.
Other mistake: Legasov is told that a 30km zone will be evacuated, shown as an ill-founded cabinet decision. Legasov himself proposes a 200km zone. At the end of the episode, Legasov appeals to Gorbachev (General Secretary) and asks him to evacuate 2600 square kilometers. It's easy to check that this is a 29km radius circle, nothing like the 200km he proposed.