The introduction of some of the more prominent Baltimore Gun Club members, and the detailing of the various bits of anatomy each of them has had blown off and replaced.
The nine Gemini astronauts all being instructed to check into a hotel under the name "Max Peck." When they meet inside, the ones who don't know each other start to introduce themselves until one finally repeats "Max Peck," since there's no point in a secret codename you're not going to use. This prompts the rest to jokingly backtrack and "correct" the names they'd given.
The astronauts of Apollo 9 name the LM and the command module "Spider" and "Gumdrop" because of the legs and the blue wrapping it came in, respectively. Apollo 10 picked Charlie Brown and Snoopy. (They stopped letting the astronauts name them from scratch after that.)
When it's time to deliver the LM to Houston, the camera pulls back from the Grumman offices as Tom Kelley and his assistant leave... showing dozens of pink Spaldings littering the rooftop.
The pre-flight LM testing, set to the theme of The Great Escape while over and over, the astronauts flick one switch or another and the power shuts off.
From episode 6, while discussing what Neil Armstrong should say when he takes his first steps on the Moon.
Michael Collins: "If you had any balls, you'd say 'Oh, my God, what is that thing?' then scream and cut your mike."
Upon cutting the engines of Apollo 12's Intrepid and crashing all of three feet to the surface:
Pete Conrad: "Shit."
Conrad and Al Bean: "WOOHOO!"
Emmett Seaborne is reporting on the Apollo 12 landing. He refers to Neil Armstrong's "immortal words" on Apollo 11 and solemnly wonders what Pete Conrad will say to mark this historical moment. Conrad steps onto the lunar surface and exclaims, "Whoopee! Man, that may have been a small one for Neil, but that's a long one for me!" Cut to Seaborne looking very flustered and having no idea what to say about these words.
Let's just say the entire Apollo 12 mission was this.
When Frank Borman becomes sick during Apollo 8, Chris Kraft has a rare moment of levity and remarks with a smile that "Man, it's gotta smell bad up there."
The general bewilderment when John Aaron recommends "Try SCE to Auxiliary" after Apollo 12 is struck by lightning.
Truth in Television: SCE to Aux was an obscure switch that was only known by John Aaron and Al Bean because of a similar failure that was run in a training simulation a year earlier. No one else in Houston or on Apollo 12 knew what it was.
While Alan Shephard is chewing out an astronaut in his office, his secretary flicks through a selection of photographs of Shephard in various facial expressions. She selects a particularly grouchy black-and-white portrait and slots it into a frame labeled "Today's Mood." A pilot coming in to talk to him sees the picture and decides it can wait. (Bonus points for being Truth in Television.)
David Scott is pretty unenthusiastic about lunar geology until Cool Teacher Leon Silver is enlisted to give the astronauts a unique crash-course. Once it's done, Scott starts gushing enthusiastically about his ideas for even more ambitious science, while Deke Slayton looks bewildered at the geological jargon being thrown at him.
The argument between the lunar geologists and the NASA science specialist over whether or not to abandon a stuck drill quickly devolves.
"You wouldn't know a vesicular basalt if it landed on your head!" "How dare you!"