Tanz says "W-We don't need one small step for man, we need the giant leap for mankind right now." That was referring to Neil Armstrong's quote on landing on the moon.
Amanda says Annie Hall. Annie Hall is a 1977 American satirical romantic comedy-drama film directed by Woody Allen from a screenplay written by him and Marshall Brickman. Annie Hall invokes stereotypes to reinforce and dispel prevalent cultural stereotypes. Hence, the mention of cultural stereotypes by Liam brings the reference of Annie Hall.
The title of the episode "Truth or Darius" is a pun on "Truth or Dare", implying that what Darius is doing is "dare", instead of truth.