Factual error: When Ryan enters the space station and removes her spacesuit she is shown wearing only a tank top and boy shorts. In reality, according to NASA's official webpage astronauts wear a liquid cooling and ventilation garment and an absorption garment (space diapers) under their suit.
Factual error: The shuttle's original mission was to service Hubble, yet when the shuttle is wrecked, Kowalsky moves with Stone to the ISS, which just happens to be "a short hike away." Hubble orbits at an altitude of 350 miles/560km, while the ISS does so at an altitude of about 250 miles/410km. Furthermore, even if they had been able to see the ISS from Hubble's orbit, they would have only seen it speed ahead, as their orbital velocities are very different: 7.66km per second for the ISS and 7.5km per second for Hubble.
Factual error: When Sandra Bullock and George Clooney manage to get to the ISS, she gets entangled with some ropes and manages to grab Clooney's safety rope. Clooney's speed should be very close to Bullocks' and the ISS', hence. The parachute ropes should be able to withhold the forces of deceleration (the mass of two people is very small, compared to Soyus or ISS), so no more pulling or having to sacrifice himself... This is due to the fact that there's no drag in space to constantly change Clooney's velocity (revert to Newton's First Law).
Factual error: When the Chinese space station is de-orbiting, and the atmosphere is stripping parts off the outside, Dr Ryan Stone is inside with objects floating about her. In reality, there would be a small deceleration caused by the atmospheric drag that would pull all objects to the front of the craft.
Factual error: When Stone makes her transfer from the Soyuz emergency escape system to the Chinese Station, she takes 3+ minutes from fastening her helmet to being inside the station. Her space suit does not include an oxygen supply. Only residual air (from the Soyuz spacecraft) is available to her, and a lot of action occurs. She couldn't do it. Too long a time, too little air. The Sokol spacesuit portrayed is intended for intra vehicular operation and requires external sources of oxygen and ventilation to be functional (as depicted in scenes before).
Factual error: During the first few minutes, before all the comsats get taken out by the debris storm, conversation between Houston and the Space Shuttle include Quindar tones. Quindar tones are the sharp beeps attending each voice transmission. These tones are obsolete and haven't been used for many years.
Factual error: Ryan states to Matt that her O2 pressure is low (which is the oxygen in her suit) just as they are about to reach the International Space Station and Matt points out she still has oxygen in her suit. Then as Ryan and Matt launch themselves onto the International Space Station, Ryan keeps panicking, hyperventilating and breathing heavily for the next few minutes and eventually she runs out of O2 as she starts to climb into the station. If Ryan only had CO2 in her suit and she had been heavily breathing for that long, she would definitely have run out of oxygen within a minute, she would never have gone this long without it.