Audio problem: When Abbie is trying to get Pacey's signature and says, "I'm collecting signatures," the movement of her lips doesn't match the speech. (00:15:05)
Continuity mistake: The first time Abby reads the "mystery letter" out loud, she says "But sex changes everything." The second time, she reads, "But having sex changes everything."
Answer: It's the same apartment Joey had in NYC. Comparing it to the beginning of the Finale; you can tell it's exactly the same location, furnishings, Plasma TV etc. Apparently Chris was only living with her at HER apartment, and now Pacey has taken his place at the end. I guess this implies Pacey successfully started his own restaurant business in NYC as he had dreamed, to be with Joey.