About 40 minutes in, when Boris Shcherbina receives a phone call informing him that the radiation had been detected in Sweden and Germany had banned children from playing outside, the program implies this was the reason he decided to evacuate Pripyat.
The scene is set on Sunday, April 27th, the correct date that the Soviets decided upon and completed the evacuation of Pripyat.
However, it was not until the day AFTER the evacuation (Monday, April 28th) that the Forsmark Nuclear Power Plant in Sweden detected the radiation. Closure of children's playgrounds in the Frankfurt region in Germany (1600 kilometers away) took place at least a week later, in May 1986.
There was at no stage the risk of a multi-megaton thermonuclear explosion during the Chernobyl disaster. There was no risk of a nuclear explosion of any kind, not even in the low kiloton range. However, this was not known at the time. The numbers circulated were taken from estimations made at the time by Soviet physicist Vassili Nesterenko, a Ukrainian who was active in the intervention to solve the crisis at Chernobyl. They reacted based on their fears of what could occur.
The American news report announcing the disaster from Peter Jennings is shown as being broadcast on 27 April, one day after the disaster. However, the radiation had not been detected yet in Sweden by this point. This report would air 28 April 1986.
During the evacuation announcement, there is a bird's-eye view scene in which we can see the rooftops of the apartment buildings in Pripyat. There are no TV antennas on any of them, and there should have been a lot. Every apartment building rooftop in Eastern Europe at the time was filled with antennas, since cable and satellite TV were not yet available.
Legasov and Shcherbina appear to travel from Moscow to Pripyat by Mil Mi-8 helicopter, which is too far a distance to reach by helicopter and would have been impractical, being much slower than an airplane. However, they are merely shown leaving an unspecified military airfield, which could have been in Kyiv after they flew on there on a plane, before embarking on their overhead tour of the disaster area.