John notices what Aeryn is wearing--
J: That’s my underwear.
A (reaching back to see the tag): What does this say?
J: Calvin.
A: Well, they're not yours.
This is fantastic, subtle reference on the part of the writers to a scene in the 1985 movie "Back to the Future."

J: What about you girls...sex dreams?
Oh, wouldn't the boys love to know that...

J: Delvian coup d’etat. Didn’t think you people had it in you.
A coup d'etat is the sudden overthrow of a government by a usually small group of persons in or previously in positions of authority - courtesy of Dictionary.com

J: So what are you supposed to do? Serve as the poster child for the revolution?
A poster child is someone who stands up as a spokesman for a cause they believe in. A site fan wrote in to let us know that poster child also implies a certain amount of good looks and manners, and would suggest certain innocence, ignorance or naîvete regarding the said cause on behalf of the said poster child. That said you can really feel the sarcasm in this one.

Z: As we train for purity, Delvians often become vulnerable to their own dark impulses.
J: (nodding at Pa’u Tuzak walking past) Is that what happened to our man Pa’u Loony Tunes?
Reference to the Loony Tunes cartoons

J: The part of ‘Tahleen’ in tonight’s unity will be played by John Crichton.
This is a pretty standard way to introduce an actor who is filling in for someone else in a play.

To Zhaan--
J: Bock bock bockawk! (Crichton makes chicken squawks.) Your translator microbes handle that one?

J: Oh, my. What is that?
Z: Unity.
J: It’s like...Disney on acid.
Disney is probably the world's most famous maker of cartoon films....and personally I think they were all on acid when they made Alice in Wonderland.