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 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: There are several scenes which depict space debris reaching the astronauts' location, with catastrophic results. While the impact of these collisions are probably realistic, it's highly improbable that this debris would be visible (you can spot many objects approaching, missing or hitting Sandra and George's location) mainly because of their ultra high speed relative to the astronauts' area. Remember, we are talking about orbits with speeds in the order of several 10k's of km/h.
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: 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.
Factual error: Space debris from an exploded satellite orbiting the earth catches up with Ryan every 90 minutes (as she goes from the Explorer to the ISS to the Chinese space station, all roughly at the same altitude). This is physically impossible. To do this, the debris would have to be traveling fast enough to catch up with the orbiting space stations every 90 minutes. However, objects orbiting at different speeds must travel at different altitudes. The faster the orbit, the lower the altitude. So it would be impossible for the debris to "catch up" with the space stations three times. Even if the two were moving in opposite directions, they would collide once every 45 minutes, as the ISS' orbit period is 90 minutes.
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 minutes left of the 90 minutes.
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.
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.
Factual error: When Stone makes it to the Chinese station, it is experiencing reentry. This is nothing but a drama-making mistake, as the station would have needed to have been actively boosted down/slowed down for it to have been a deliberate deorbit, or have had its navigation completely neglected for months or years for its orbit to decay to that point. In either of these two cases, it could not have been orbiting at a fixed position with the otherwise-stable ISS.
Revealing mistake: In the Soyuz capsule, Ryan attempts to break the parachute stuck to the station off the capsule. After she gives up, Ryan switches off a beeping alarm and says "Great." To Ryan's left (or viewer's right), there is a sticky note visible and a pen visible. The note is reflected in the window, but the pen isn't.
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: 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.
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 digital radios operate on a different, highly stable technique for tuning, and do not produce heterodyne sounds.