The Saturn V service structure disappears and reappears during the launch countdown
The rocket used for the XRV launch switches between a Titan IIIC (with solid rocket boosters on the side) to a regular Titan II (no boosters) from on the pad to lift-off.
The stripe on Dougherty's helmet momentarily disappears while he is flying the XRV-1
Powerful arc lights are seen being switched on in sequence, and they light up the Vehicle Integration Building (VIB), which is recognizable by its 4 large doors, side by side. This is where the Titan boosters are assembled, one of which was to launch Dougherty in the XR7. However, this takes place after the titan has already been seen being moved out the launch pad, and so this sequence wither is superfluous or should have been placed earlier in the film.
The Mediterranean coastline as seen from orbit on several occasions barely resembles the correct geography. Spain is distorted and the Strait of Gibraltar is almost unrecognisable.
The astronauts repeatedly are shown releasing free-floating hand-held objects such as video cameras during their spacewalks. However, no loose untethered objects are ever allowed on spacewalks as the potential for them to float away and become hazardous objects is too great.
A Saturn V rocket would not be necessary for a spacecraft bound for low-Earth orbit. A more preferable choice would have been a Saturn 1B.
The Earth as represented in the on-orbit shots is too small if the spacecraft is supposed to be in Low Earth Orbit (approx 200 miles) as would be expected for an orbital laboratory (and Voskhod) mission. The apparent altitude is more like 1000 miles.
The Russian Voskhod spacecraft depicted only shows the spherical re-entry module. The service module is missing.
When Astronaut Lloyd does his "acrobatics" with the rocket pack, the sunlight is hitting his right side. However, when he makes a 360 degree turn, the sunlight remains on the right side of his suit no matter what position he is in during the turn.
When Astronaut Lloyd does his "acrobatics" with the rocket pack, he ends his 360° rotation by pushing the joystick control in the same direction he used to start it, which should have made him rotate faster.
In the external shots of the spacecraft orbiting the Earth, the sun rises and sets, but the stars in the background do not move.
When an astronaut dies in the line of duty, the task of informing the surviving spouse is always carried out by a fellow astronaut, and in person. Given Director Keith's workload and the seriousness of the crisis, this duty most certainly would have been delegated to an astronaut on site in Houston, and not performed by Keith via telephone as depicted in the film.
When Buzz Lloyd starts laughing, he is shown straight-faced. When the camera angle shifts he can then be seen actually to be laughing.
The Apollo Service Module's main engine used Aerozine 50 and Nitrogen Tetroxide - the same as in the Ascent Stage of the Lunar Module. A major reason for the choice was that they are hypergolic, meaning that they ignite on contact, and therefore do not require any form of ignition system, making its operation much simpler and effectively making a failure impossible. throughout the Apollo, Skylab and Apollo-Soyuz programs, there was never a single failure of the Service Propulsion System or the Lunar Module Ascent Stage..
When Keith announces the time for the launch through the eye of the hurricane, he says, "We are go for launch at 22:31:06 local time." Moments later, the doctor privately tells Keith, "Of course, you know that by 22:31:06 the crew will be dead. There's not enough oxygen for three men to live that long." They then discuss whether two men can survive.. or even one. However, Keith does not even talk to astronauts about this situation until AFTER the launch, when the men should already be dead.
The arrival of the hurricane eye and the corresponding launch window in real life would have been anticipated, expected, and planned for.
When being advised about making a second attempt at re-entry, spacecraft commander Pruett says that they will do this by firing the RCS - the Reaction Control System. This refers to the 4 sets of thrusters (quads) fitted to the Service Module. He presumably suggests this as the engine from the SPS - the Service Propulsion System - had failed to ignite as planned on the first attempt. However the SPS engine has a thrust of 91 kN, and each of the RCS engines only has a thrust of 100 N. Even with an engine from each of the 4 quads firing together, their combined thrust would only be 400 N, less that 1/200 that of the SPS, and completely inadequate to bring the Apollo Command Module down.
Commander Pruett suggests shutting down two of the fuel cells to save electricity, saying that they can start them up again later. However the fuel cells do not use electricity - they produce it. They work by combining oxygen and hydrogen to produce electricity, and a little water. This is the reverse of electrolysis of water to produce oxygen and hydrogen. However shutting down the fuel cells is done by closing the reactant valves, and this is a one-way action as the valves cannot be re-opened except by technicians on the ground accessing the equipment.
As the Apollo spacecraft approaches the orbital laboratory, one of the crew reports that their speed is 50 feet per second. This means moving at a distance just over twice the length of the Apollo's Service Module every second. The view in the film is that the craft is moving considerably slower than this, closer to 5 feet per second, which is far more accurate.