Factual errors: As pointed out by one of the characters, the ship enters the "blackout" area around the sun (and loses contact with Earth) anomalously early, before Mercury's orbit in fact. Communications from this close to the sun are not a problem in reality (and were possible with 1970s technology), but the writer and director took deliberate creative license to improve the tension.
Factual errors: In his DVD commentary, director Danny Boyle says the original idea for Icarus I was to "be on its side, like the Zeebrugge". In fact, he is referring to the "Herald of Free Enterprise", the British ferry that capsized on 6 March 1987 while leaving the Belgian port of Zeebrugge. 193 passengers and crew were killed.
Factual errors: When the crew are stuck on Icarus 1 and are about to jump out of airlock without the spacesuits, one of them mentions that the temperature outside is -273 degrees. Due to the background radiation the lowest temperature in space is approximately -271 degrees and it would in fact be higher than that due to the proximity of the sun.
Factual errors: When we see Mace's frozen body, it's covered with a thin sheet of ice. However, the computer coolant is a very cold liquid which could not spontaneously freeze solid by itself. His body would have appeared frozen stiff but still very wet with the same coolant still in its liquid state.
Factual errors: As the crew attempts to rotate the shield to repair it, there is an argument that they would lose com towers 3 and 4, which they say would need on the way home. However, many shots including the simulation of payload delivery reveal that the Icarus' small shield which is supposed to protect Icarus after the payload is detached, just isn't wide enough to protect those towers at all, so they would've lost them anyway. It is even questionable, whether this shield would be capable of protecting the Icarus itself after detaching the payload with the large shield and at that close distance from the sun.
Revealing mistakes: In this movie, like in most science fiction productions, sound is heard in space. This is impossible due to the absence of a medium that can transmit sound in the vacuum of space. (However, audiences have grown so accustomed to this error, it is hardly an option for any sci-fi production to stay true to the laws of physics in this case.)