We see the launch of astronaut Lee Stegler's solo trip to the moon in a standard Gemini capsule atop a Titan II launch vehicle. However, when showing the Gemini capsule on the moon, it sits atop large square descent stage that extends several feet beyond the diameter of the capsule. The descent stage would have been visible protruding from the capsule and launch vehicle during blast-off, but was not.
When explaining the medical telemetry to Mickey Stegler, the doctor says one plot is respiration and another is breathing, even though both words mean the same thing. Also, several of the plots have completely different shapes from what they should.
After landing on the moon, astronaut Lee Stegler normally walks on the moon surface, just like walking on Earth. Moving in the lunar gravity, one-sixth of Earth's gravity, is a process of loping, including two-footed kangaroo hops. The fine moon soil is quite slippery and the real-life astronauts who actually walked on the moon reported that they needed to plan their movements six or seven steps ahead.
Stegler's helmet has no sun visor, which is critical in space.
When he is at the Russian lunar crash site, in the close up you can see a drawstring from his spacesuit covering at his helmet is clearly blowing in the breeze. This happened because they were on an outdoor location whereas on the actual lunar surface there would be no wind to blow the drawstring.
Lee is supposed to be in a vacuum chamber checking out the lunar habitat module, but a close look at his space suit reveals he is wearing pants (made of impossibly thin material) and there is a gap between them and his boots where another thin layer of material is visible (socks?).
The weightless flashlight has a very obvious suspending thread attached to it. Possibly the most obvious example of this classic space mistake known :)
When James Caan is sitting in his car outside the space center building, a shadow and reflection of the crew/boom mike can be seen on the car.
The story takes place in Florida but there are hills and low mountains in the background of many exterior scenes (except for the ones actually showing launch pad at the NASA Space Center at Cape Canaveral). The highest elevation in Florida is only 345 feet and it is only 10 feet above sea level at Cape Canaveral.
In scene of Lee's walk on the moon just before finding the shelter, desert plants are clearly visible in the background casting shadows.
Chiz and Lee are depicted as landing in a USAF Northrop T-38A. In the landing shot, the plane has a tail number of 64328. However in the taxiing and parking shots, the plane's tail number is 10475.