In this series, the "White Room" - the small room attached to the Apollo landing gantry, which the crewmembers pass through on their way into the capsule - is the real thing. It was discovered in a forgotten NASA storage room, taken out and used in filming.
The lunar module (LM) seen in several episodes up close, is in fact a real lunar module. It was originally scheduled to go to the Moon as part of the Apollo 18 flight; NASA budget cuts forced Apollo 18's cancellation, but the LM was saved and eventually used in filming this miniseries. It is now enshrined in a museum. In some episodes, we can see a bus-like craft which takes the astronauts from NASA down to the pad at Cape Kennedy just prior to launch. This bus is also the real thing, which the real astronauts all used.
Three actors who played astronauts also played astronauts in Apollo 13 (1995), but they all played different astronauts from the ones they had before. David Andrews played Frank Borman (Apollo 8) in the miniseries, but Pete Conrad (Apollo 12) in the movie. Ben Marley played Roger Chaffee (Apollo 1, died in the fire) in the miniseries, but John Young (Apollo 10, Apollo 16, Shuttle) in the movie, and Brett Cullen played Dave Scott (Apollo 15) in the miniseries, but Jack Lousma (CAPCOM during Apollo 13, slated for Apollo 20 which was cancelled, flew Skylab 3 in 1973) in the movie.