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.
The helicopter crash did happen in real life and in the same way as depicted. However, in real life it happened several months later, on 2 October 1986.
Khomyuk states that iodine 131 is a decay product of uranium 235. Iodine 131 is a fission fragment. It is among the elements left over when an uranium 235 atom splits. The decay product of uranium 235 is thorium 231.
There was at no stage the risk of any thermonuclear explosion or any explosion even approaching the megaton range during the Chernobyl disaster. There was no risk of a nuclear explosion of any kind, at any stage not even in the low kiloton range. And every actual expert involved in the recovery at the time of the accident was fully aware of this because it is physically impossible for a nuclear explosion to occur by accident within the molten remains of a former reactor core. You need highly enriched fission fuel to achieve that, which was not present in the core even before the accident. If anything, the fuel was being diluted by molten concrete and non-fissionable reactor metals in the accident. But even if it had all been 100% weapons-grade material, you would also need a complex mechanism functioning with extreme precision to not only create a supercritical mass but keep it assembled and highly compressed for long enough to release the explosion energy before it blows itself apart. This simply cannot occur by accident and every person with a modicum of scientific literacy knew that even at the time.
About 35 minutes into the episode, the helicopters starting the air-drop operation are shown carrying their loads in cargo-nets. In real life, for the first days of this operation the flight engineers had to push out the sand-sacks by hand. The parachutes that were later used as cargo-nets arrived only on Wednesday.
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.
In the shot with the helicopter in the smoke plume, the smoke shows no interaction with the helicopter's main rotor, revealing it to be CGI. The rotors should be causing enormous turbulence.
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.
When the three men enter the flooded area in dry suits, to open the slice gates, their respirators are not connected to their face masks.
In the morning of April 26, the Byelorussian Institute in Minsk is shown almost empty, with only a couple of workers present. It was Saturday. In communist countries, Saturdays were not days off. People were supposed to be at work.
When General Pikalov is being decontaminated, his hood is left dry while everywhere else is cleaned.
The flag on the Minsk Obkom is a flag of the Republic of Belarus, not the Byelorussian SSR.
Subtitles in Ep2 refer several times to Plant Director Bryukhanov when in fact the dialog is referring to General Pikalov.
At 0:37, Shcherbina instructs the radio operator to tell the helicopter pilots that they must approach the reactor from the west. But the winds have been blowing from the east and SE, blowing radiation to Sweden and Germany. The pilots should have approached the reactor from the east so the wind would blow the sand and boron toward the reactor.
Quite consistently, throughout the series and by different characters, Geiger counters or similar radiometers are referred to as "dosimeters." For example, at 10:52 in this episode Legasov speaks of "low-limit dosimeters" and at 26:00 Gen. Pikalov says that their "high-range dosimeter just arrived."