In the movie the space shuttle is running with a speed that caused the broken ribs of the cosmonaut. In real life the movement is much slower than shown.
In the movie regular doctors from regular hospitals are sent to the space station in order to do the medical operation. In real life only doctors who have experience with operations in zero gravity can be sent there due to the experience.
When Evgeniya tells Vladislav "I love you" her lip movements don't fit to the words that are heard.
Yevgeniya is sent to space despite barely haven't done any tests that real cosmonauts and astronauts are required to do, which the other contestants in the movie actually did. She also didn't participate most of the training and only got the basics, which is not enough for going to space.
In the movie the doctors prepare the important operation on the lungs and rips for a month but in space they just use ordinary wire and a spoon, which would not be very practical.
A character said that in 60 years of space travelling humanity only traveled 400km away from earth. It is not true, as the distance between the earth and the moon is around 384 400 km.
Konstantin Volin mentioned that Sergey Koroljov, a famous Soviet Rocket Engineer and the builder of the Soyus-shuttles, was considered crazy and he was being laughed at. In real life he was considered a talented and respected aircraft-builder in the late 20s being a student.