Revealing mistake: When Dyatlov goes outside the control room to check on the situation after the explosion, his collar and button strip on both his shirt and coat change positions. When he's in the room, it's facing his right, but when he leaves the room and see graphite on the ground below him, it's facing his left.
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.