Lynette Squeaky Fromme and Sara Jane Moore's attempt to assassinate Gerald Ford. The key word here being "attempt". Even Gerald Ford had to step in a help them pick up the fallen bullet.
One of the performances has a subdued one shortly before that: As Moore sings "This one was on sale! No, not the shoe! Well, actually, the shoe was, too!", Guiteau nods with a face of complete disinterest and exasperated annoyance. In the same version, as he mentions "Promote the sale of my book", he pauses the song to inform the audience that "Copies are available in the lobby".
The ending of the scene really stands out. Squeaky and Moore thank the friendly man for helping them pick up their bullets, and he introduces himself: "Gerry Ford." The two women stare at each other... then the Secret Service who have been right there the whole time. When Ford leaves, Sara attempts to throw the bullets at him. Then the buzzer goes off.
Moore: SHIT!
Even better? As she's throwing the bullets at him, both women start yelling "BANG! BANG!"
The entire scene - especially Fromme's increasing exasperation at Moore having brought her dog and her young son to an assassination. Turned up to eleven when the kid starts pestering his mother for money for treats, which she refuses to give him, so naturally he starts wailing until Moore points her gun at him to shut him up.
Ditto for Hinckley's attempt to kill Ronald Reagan. Supposedly this was also Ronald Reagan's answer to Jimmy Carter in the debates.
Reagan: There you go again. There you go again. There you go again.
All of Reagan's responses in the play are from actual quotes from when he was actually shot.
Sorry, Nancy. I forgot to duck.
I hope that surgeon's a Republican.
Where'd that kid learn to shoot, the Russian army?
Zangara:(groaning in pain) Booth: You know, you really ought to do something about that stomach. Zangara: I do everything about this stomach! Booth: Oh, yes? Zangara: I give up wine. No good. I give up smokes. No good. I quit my work, no good. I move to Miami! No good! I TAKE APPENDIX OUT! NO GOOD! NOTHING, NO GOOD! NOTHING! NOTHING! NOTHING! Booth:Have you considered shooting Franklin Roosevelt? Zangara: ...You think that help? Booth: It couldn't hurt.
Anything Guiteau says or does when performed correctly, especially when he brings up his book.
That saying actually originated after Massachusetts was the only state to not give its electoral votes to Nixon. Hilarity ensues when Byck reveals two seconds later that he actually voted for Nixon.
Depending on the performance, the extent to which Booth gets annoyed with the Balladeer can be funny to watch too, especially if it's played as the Balladeer deliberately trying to make him snap.
The Proprietor's line during "Everybody's Got The Right" which also introduces Sam Byck:
Proprietor: Everybody's got the right to be...different...
(Byck enters dressed as Santa and carrying a protest sign)
Proprietor: Even though at times they go to extremes.
Pretty much anything Lynette "Squeaky" Fromme says, but especially whenever she goes into one of her "Charlie says..." rants.