Continuity mistake: Right before the graduation service, Dawson is joking with Joey to get her mind off her speech. The wind has blown Joey's tassle so it's caught partly on her left ear facing the camera. But in the next shot of her, the tassle is suddenly hanging normally in front of her ear. She hadn't appeared to move her hands.
Continuity mistake: During this scene towards the end, Bessie insists on putting lipstick on Joey for Graduation. She dabs it on quickly, and there appears to be a noticeable smudge or mark on Joey's upper right lip from the lipstick. But the next shot of Joey, the lipstick suddenly appears normal and perfectly applied, and the smudge is gone. (00:33:40)
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.