Audio problem: When Dawson's father hands the baby to Joey, so he can take a picture of her and Gretchen before the Prom, you can hear a noticable "Ahhhhhh" in a female voice from the background, that sounds very much like Dawson's mother. But this wouldn't make sense, as Gail had just gone off to find her shears and cut roses for the corsages.
Continuity mistake: When Joey and Pacey are talking at the table on the Promboat after the 'brutal breakup'; her arms keep changing position too quickly between shots. As Joey says, "You break my heart into a thousand pieces," her right arm is folded across her, and the right hand is resting on her left sleeve just below the bare shoulder. The next shot, from behind Joey you can see her right hand still gripping her left shoulder, but the sleeve is further up and ruffled on that side. Then just before she says "Just leave me alone", the next shot again shows Joey from the front; and suddenly her left arm is raised up, hand by her face, and the right arm is down on the table with the hand curved up in the air. As she says "Just leave me alone"; her left arm is still up and hand resting by her face, and the right arm is laid sideways across her, hand on elbow. Then the next shot of Joey shows that suddenly her pose has changed; and her left arm is raised up diagonally, hand across her right shoulder, and her right arm is still laid horizontally across her, hand by her elbow. All of these transitions are far too abrupt and fast to be realistic.
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.