EMILY: I have to get out everything she’s [Richard’s mother] ever given us. Thirty-five years worth of fish lamps and dog statues, lion tables, and stupid naked angels with their … butts!
LORELAI: Whoa! Stupid naked angel butts? What, did David Mamet just stop by?
Lorelai is probably referring to David Mamet’s 1983 play Glengarry Glen Ross. It shows two days in the lives of four Chicago real estate agents prepared to do anything, no matter how illegal or unethical, to sell some undesirable real estate. It won the 1984 Pulitzer Prize, and in 1992 was made into into a highly-acclaimed film, with the screenplay written by Mamet.
The play is notorious for its use of profanity, and Lorelai is teasing her mother for her uncharacteristic use of the word “butts”. Maybe the butt model conversation affected her.
David Mamet is one of Amy Sherman-Palladino’s own favourite playwrights.
Emily’s statement suggests that she and Richard have been married for thirty-five years, so since 1965-1966.