Ozzie Mandril references Marvin the Martian when he says, "Where's the kaboom? There's supposed to be a Caribbean-shattering kaboom."
The character of Judge Tripps is named after longtime LucasArts employee Jo Ashburn, whose nickname is Capt. Tripps.
That the Scumm bar changes name to Lua Bar is a reference to the fact that the three previous games were programmed in the SCUMM engine. Escape from Monkey island was programmed in the GrimE Engine, a program made in LUA script.
The only Monkey Island game to not have Alexandra Boyd as the voice of Elaine Marley. This also explains why this is the only game in the series where Elaine speaks with a Northern-American accent instead of a British one.
The reference to the Anti-LeChuck having 1138 stamped on his forehead is a reference to George Lucas's early film, THX 1138 (1971). Also, in the swamp on Lucre island, one of the choices for the number Guybrush is thinking of is 1138.