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.
Continuity mistake: Just after Matt retrieves Ryan, Matt tells her to set her watch timer for 90 minutes, which she then does. A shot is then shown of Ryan's arm adjusting the watch timer to 90 minutes and the time on the watch reads 00:32. Later on, when Ryan is in the Soyuz capsule, she looks at her watch and says "Seven minutes to get out of here." It is shown that the time on her watch reads 02:21 (1h 49m later) but the timer reads 7 minutes and 26 seconds left of the 90 minutes.
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).
Continuity mistake: After the rope keeping Ryan and Matt tethered together is snapped, Ryan continues drifting downwards towards the Earth. The shot continues panning until the camera stops with the camera high up. As she falls, the ropes from the parachute around the satellite are on Ryan's right. In the next shot from low down, the ropes from the parachute have moved to Ryan's left. She was only shown spiralling downwards throughout the shot, so her position next to the ropes would not have been affected.
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.
Continuity mistake: On the way to the ISS, Matt asks Ryan where's home. Ryan replies "What?" and Matt says "Down there. Mother Earth." Behind Matt as he says this is the rope keeping Matt and Ryan tethered together drifting around. At the end of the shot, the part of the rope shown in front of Ryan is shown to be drifting around differently to when it cuts to a shot of Ryan.
Continuity mistake: Just as Ryan and Matt are about to bump into Shariff's body, the POV shot of Ryan shows Ryan shielding her face with her hands. It can be noticed her right hand is positioned in a shifted 10 o'clock direction. Instantly as soon as the next shot starts, her right hand is now in a 12 o'clock direction, not shifted at all.
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.
Audio problem: In several scenes, Sandra Bullock used radio equipment in efforts to call for assistance. There is a sound made by vintage, mechanically tuned radios called "heterodyning" that results in a squealing, variable frequency sound in the speaker. While heterodyning added a degree of drama to the scenes in "Gravity", contemporary radios operate on a different, highly stable technique for tuning, and do not produce heterodyne sounds.
Visible crew/equipment: In the Chinese Space Station, Ryan climbs into the Shenzou capsule and seals the airlock behind her. As she seals the airlock, you can see the shadow of the camera to the left of the screen on the wall, moving around. There is nothing there in the station that could have possibly made the shape on the wall. The shadow cannot be a piece of paper as it is not the same size as the shadow shown in the shot. Nor can it be any other object in the module as it is moving at a much different pace than all other objects shown in the scene.
Continuity mistake: When Ryan and Matt reach the ISS, as Ryan says "Wait, you have to brake!" the ISS is visible from the POV of Ryan. About two shots later, another shot of the ISS is from Ryan's POV, only now they are way further away from the ISS than they were two shots previously. The second shot may appear a bit confusing because it is at a different angle, but they are definitely much further in the second shot.
Audio problem: Ryan is on the International Space Station and looking through the window in an attempt to communicate with Matt. During this transmission, Ryan says "Please talk to me. Please." When she says "Please" the second time, her lips move before the word can be heard. Her lips are very visible through the reflection of the window.