On learning many communications satellites have been destroyed, Kowalski remarks, "Half of North America just lost their Facebook." The Internet doesn't use satellites but instead high-speed landlines and microwave relay towers, so Kowalski was either misinformed or making a joke, but either way the Facebook statement is incorrect.
Stone has not yet found the ISS hatch while Kowalkski continually talks to her. Despite knowing she is absolutely out of air, with CO2 poisoning beginning, she stops trying to save herself to listen, and doesn't resume until he finally stops. While he might have been trying to keep her awake, he almost certainly would have had her describe what she was doing in an ongoing commentary, so he could tell if she started drifting off.
After the Chinese landing pod is separated from the rest of the station, all the pieces are shown burning hot from the air friction, which indicates the re-entry stage. It is when the Soyuz-type vehicles are under quite a few G's of braking force - anything but weightlessness. Yet the helmet and other items seem to be freely floating inside the module, which is physically impossible.
Kowalski is shown joyriding around the Space Shuttle while repairs on the Hubble Space Telescope are taking place. Three reasons why this would never happen: it's unnecessary (meaning it would never be planned, meaning it would never happen); it's unsafe, risking collisions with the HST and/or Space Shuttle; the exhaust from the propulsion pack would risk fouling the optics and instruments of the HST.
When Stone removes her spacesuit it is missing two parts, one of them being the Liquid Cooling & Ventilation Garment. The LCVG is what keeps astronauts from overheating and cannot be left out. It also deals with sweat. Without it Stone would risk a heat stroke. She'd also be soaking wet considering her extreme exertion earlier in the movie. We see none of that.
It is hard for most people to understand the difficulty in being in orbit trying to reach another object in orbit. Accelerating an object in the direction of travel will actually not move you forward. Instead the energy is used up raising the object's altitude, where it will have a slower orbital speed and therefore actually move "backwards" in orbit. Accelerating "up," "down" or "backward" would have other results that most people wouldn't expect. For Stone to directly aim at the Chinese space station in its own independent orbit and accelerate in that direction would give results that are unpredictable given our lack of knowledge of both orbits, but most definitely would not result in her getting to where she wants to go.
Kowalski estimates they have 90 minutes before the debris field completes an orbit and threatens them again. That's not at all how things in orbit work. The original Russian satellite traveled in its own (presumably low-Earth-orbit). Assume it exploded with great force. The debris by definition would be sent into every direction, the density of objects attenuating by the cube of the distance the debris traveled. It would be very unlikely for any debris to reach the Shuttle, ISS or Chinese space station, or even other satellites. The film shows huge numbers of pieces hitting all at once, despite the debris being the result of multiple collisions separated by time, distance and original orbital track. No matter what, the debris would be in a completely different orbit from the ISS, and would not return.
The Space Shuttle Explorer is in the same orbit as the Hubble Space Telescope, which is being repaired. While both the International Space Station (and presumably the Chinese space station) are in orbit at the same approximate altitude (roughly 200 miles above the surface), they are most definitely not in the same orbit. At any one moment they could be over opposite parts of the Earth heading in opposite directions. Their orbits are specifically picked so as to never put them near each other, with one never directly in front of the other. Finally, since all objects in orbit circle the center of Earth's mass, they can't parallel each other, either, so the distance between them would be rapidly increasing or decreasing (given how close they were in the film the latter would have been true). In any case, the amount of energy required to travel from one object to another in independent orbits and then match velocities is probably well beyond even the Space Shuttle's ability, yet in the film it was done by one orbital pack with one astronaut pulling another.
Houston tells the astronauts that debris from a Russian missile strike on one of their satellites has caused a chain reaction, destroying other satellites, and a huge debris field is heading toward them at high speed. NASA: "Multiple satellites are down and they keep on falling." Kowalski: "Define multiple satellites." NASA: "Most of them are gone. Telecommunications systems are dead." There are a great many problems with this, made all the more important because point is so central to the plot. Although NASA states that multiple satellites are "down", it would be a misinterpretation to think that the satellites are dropping from the sky. It is common technical vernacular to say that a server, or a satellite, is "down" when it is no longer functional. Conversely, a server or satellite is "up" when it is functioning - which is why we have the term "uptime". So multiple satellites are no longer functional, they are not falling out of orbit. More importantly, communications satellites aren't in low-Earth-orbit ("LEO") like the Shuttle & Hubble Space Telescope. LEOs are at an altitude of roughly 200 miles, whereas communications satellite are in geosynchronous orbits (so-called "Clarke Orbits" in honor of SF author Arthur C. Clarke who first proposed them) about 22,240 miles above the Earth's surface. It is virtually impossible for a non-nuclear explosion to send debris 22,000 miles up even in airless space, never mind put pieces on an intersecting path with satellites that travel above the equator. Third, NASA didn't always use communications satellites to reach the Shuttle. If the Shuttle was above America NASA could use microwave, telephone and other methods to send voice to the appropriate ground station, which would then beam the signal directly to the Shuttle (and vice versa). Ground stations in Europe could be reached by NASA via the telephone & data trunk lines under the Atlantic Ocean. In the worst case Ham Radio could even be used to communicate between NASA and the various ground stations. Even if none of this was possible ground stations are manned by communications people during Shuttle flights, and they could have talked directly with the Shuttle even if they had trouble reaching NASA immediately.
There are no side hatches with portholes that open on the descent (re-entry) module in either the Soyuz-TMA or Shenzhou spacecraft. It has three hatches: The ingress and EVA hatch, which is the only way of entering the spacecraft at launch; The internal transfer hatch through the docking port (not installed in all Soyuz crafts), and; The hatch to the descent module. Crew ingress takes place by the crew entering first the orbital module and then climb into the descent module. This is necessary as the descent module is simply too small to allow more than three hatches.
During the re-entry sequence, Dr. Ryan (Bullock) is oriented in the wrong screen direction (facing forward, right to left) relative to the position of the Shenzhou's heatshield facing backward, left to right).
After Stone passes the panel where the fire is starting on board the ISS, her hand strikes a drinking pouch of water. The blobs of water are mistaken by some as a stream of air bubbles, as if the visual effect of weightlessness was created using a water tank. That was not the case in this movie. The water drops are computer generated.