Tony Nelson is a very unusual astronaut in that he goes into space in a Mercury capsule, a Gemini capsule, an Apollo capsule and in the TV movie follow up in the space shuttle. No real astronaut has ever flown on all four spacecraft.
They use an Apollo mission number and 3 astronauts, but all the exterior shots are of a Gemini launch on a Titan rocket and a Gemini capsule in flight. The Gemini program only used 2 astronauts on each mission.