Paris talks to her nanny, who she previously mentioned was Portuguese, on the phone in Spanish, not Portuguese.
One of the lies Emily tells at the bar is that she "doesn't dance." In reality, Kelly Bishop was in the original Broadway cast of A Chorus Line.
Emily tells Lorelai at dinner that she and Richard stayed in Thailand when they were first married, eating hot peppers and skinny dipping. Later in the series when they are separated, Richard comments during an argument that they went skinny dipping 'once' and Emily wore an overcoat.