Goofs

The Americans never launched any of their Space Shuttles to Salyut. NASA indeed planned to send the Challenger or the Discovery to take photos of the drifting station, and retrieval was considered, but all these plans were dropped because they didn't want to provoke the Soviets, particularly not in the interregnum shortly after Konstantin Chernyenko's death, not knowing how firmly has the new Premier, Mikhail Gorbachev is sitting in his chair.

At the briefing scene a concern that the Americans may intercept the uncontrolled space station and obtain military secrets is repeatedly stated. In reality the Salyut carried no military secrets as it was a civilian installation. If the Americans wanted military secrets, they should've gone after Almaz, the today little known military version of the Salyut, also in orbit at the time. Such an emergency never happened to the Almaz though.

Challenger was indeed in orbit at the same time as the Soyuz T-13 mission but was not flying with an empty cargo bay as it flew Spacelab-2 and never came anywhere near the Salyut 7 space station as they were in two different orbits and inclinations.

Shudin lists off the four cosmonauts lost until that date in the Soviet space program, among whom he mentions "Yuri Dobrovolsky". In fact he meant Georgy (George) Dobrovolsky, who along with Viktor Patsayev and Vladislav Volkov died in 1971 on Soyuz 11 when a valve accidentally opened during the re-entry procedure and the capsule's atmosphere was vented to space.

It is said several times that if the cosmonauts can't revive Salyut, the military will have to shoot it down. In reality this was never even suggested as the Soviets had no means to destroy an orbiting space station.

The Soviets had a hunter killer satellite program from the 1960s to the 1980s. This could have been used to shoot down Salyut-7.

Fedorov suggests that they drink alcohol to warm up. As alcohol is a depressant, it would have actually lowered their body temperatures. While, relatively speaking, it would have felt slightly warmer, the reduction in their body heat in such circumstances would be potentially dangerous.

The Challenger crew is shown wearing orange Advanced Crew Escape Suits (ACES), known as "pumpkin suits," which were introduced to the shuttle program in the late 1990's. As of 1985, the astronauts would have been wearing blue Launch Entry Suits (LES).

During the fishing scene Dzhanibekov rudely insults Savinikh, calling him "not a cosmonaut, just an engineer in a spacesuit". No Soviet cosmonaut would say such a thing to his colleague, regardless of his task and status. Everybody who was certified to be a cosmonaut was treated equally, just like among American astronauts. Not even backup crews who never got to fly received any such banter.