Brie Larson, who played Rachel, actually auditioned for the role of Annie Edison, which eventually went to Alison Brie, according to an interview made by HFPA Chairman Ruben V. Nepales for his international column for the PDI Inquirer Entertainment.
Chang, as the DJ, announces that the Sophie B. Hawkins dance is sponsored by Hawthorne Wipes, which are "perfect for cleaning the dash of your '92 Subaru". In the early '90s homosexuality was less socially acceptable. But when the Subaru demographics folks realized that their Outback was rather popular with lesbians, they started the first advertising campaign deliberately aimed at the lesbian niche market. For a while the Subaru Outback was the semi-official car of the lesbian community.
The character Kat is a parody of the Manic Pixie Dream Girl. A popular film stock character, the MPDG is an eccentric, quirky teenage girl or young woman who never pursues her own happiness and only exists to help the depressed male protagonist lighten up. Knowing what a film buff Abed is, it's clear this is why Annie set them up.
When Abed leaves Jessica to go to the coat check room for the first time, he leaves behind a kaleidoscope and a Gideon's Bible, describing them to Rachel as icebreakers. These are references to the popular Beatles songs "Lucy in the Sky with Diamonds" and "Rocky Racoon."
The t-shirt Pierce is wearing while talking to Brita in the computer area is apparently the American version of the fictional Inspector Spacetime series he pitched to the focus group facilitators during the episode Conventions of Space and Time (2013) at the convention. During the focus group, Pierce pitched the idea that instead of the constable sidekick, the show should feature "a blonde with long legs and a tennis racket." Hence, the sensuous outline of the woman on the t-shirt.