The scenes at Paxton Air Force Base were filmed on location at Edwards Air Force Base. In the newscast seen at the very beginning of the episode that describes Wagner's mission, the reporter mentions that the spacecraft is launching from Edwards.
Steve Wagner says "failure is not an option". The same thing was said by Gene Kranz (Ed Harris) in Apollo 13 (1995), which, like this episode, was also about astronauts. There is also a reference to Toy Story (1995) (see movie connections). Both movies starred Tom Hanks. The fictional air force base is called Paxton Air Force Base. Bill Paxton starred in Apollo 13.
Tom Ohmer, who played a sergeant in "Mr. Monk and the Other Detective," reprises his role in "Mr. Monk and the Astronaut." There's an interesting interview with Ohmer, who in real-life is an ex-cop, in which he talks about working with Ted Levine and other members of the cast and crew.
Monk states that Joanne Raphelson (Brianna Brown) is 5'5", then Natalie Teeger (Traylor Howard) says that she is also 5'5", she then tests the stool to see if it's high enough for her to fit her neck in the noose. Both actresses are in fact 5'5" in real life.