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The suspenseful underscoring that plays while the crew attempts to build a filter is a recycled/repurposed score, originally used in The Pelican Brief (1993) when the protagonists retrieve a safe deposit box and flee attackers in a parking garage. James Horner is the composer for both films.
In a commentary track, Marilyn Lovell comments that Tom Hanks exactly portrays Jim Lovell's mannerisms and style of movement.
Bill Paxton, Tom Hanks and Kevin Bacon were all very proud of the fact that they weren't sick on the so-called Vomit Comet - the plane used to simulate zero gravity. The cameramen weren't so lucky.
In some scenes where the Earth can be seen from the windows of Apollo 13, it is one of the photos taken by Jim Lovell and Bill Anders on the Apollo 8 mission.
Jim Lovell wore his old Navy Captain's uniform in the scene where he greets the astronauts aboard the U.S.S. Iwo Jima. When Ron Howard asked Lovell if he'd like to be in the film as the ship's Admiral, Lovell agreed, but pointed out, "I retired as a Captain; a Captain I will be."