Audio problem: At the end of the episode when Pacey and Joey are paying for their items, Pacey launches into a philosophical speech. The cashier has asked him whether 'they found everything they were looking for' and he answers no, but they found what they needed, which was even more important. He then elaborates, explaining that 'if you found everything you needed that day, what would be the point of doing it all over again the next day'. But Joshua Jackson apparently messed up his dialogue, because the point he was making was that they didn't find everything they were looking for, not what they needed. He was making the point that they did find everything they needed, so it would be contradictory to then explain that there was no point in finding everything you need. He meant to say 'if you found everything you wanted (versus needed), what would be the point of doing it all over again the next day'. Oops.
Plot hole: When Pacey and Joey get locked in the Big K-Mart, they run to the front doors and start banging on them and yelling at the guard. The guard, who is in the parking lot turns back towards his car and faces directly towards Joey and Pacey in the front windows. They aren't that far from the guard's car, and he was looking directly towards them. There is no way the guard would not have noticed two full-grown adults standing in the front glass doors pounding their hands on the glass and yelling at him.
Revealing mistake: When Joey and Pacey are playing Battleship, there are a few close-ups showing their game screens. Although you can see several push-pins in each screen, signifying the areas of the game they have tried; there are no actual ships visible. It looks like they are playing the game with only the push-pins, and not any actual battleships.
Plot hole: When Pacey and Joey are in the break room, waiting for the police to call them back, they start arguing. The phone suddenly rings, and Joey asks Pacey not to answer it in order to finish their conversation. But this doesn't make logical sense; considering their desperate circumstances (being locked in the store all night) and how hard they tried to get hold of law enforcement to help them get out, there is no way Joey would not want to answer such a critical phone call. It may have been their only chance to communicate with help.
Continuity mistake: At the beginning, Pacey and Joey are dining at a large table while Pacey is flirting with the woman on his right. Joey goes underneath the table to retrieve her shoe, and sees what is apparently the woman's left hand on Pacey's knee. But the very next shot of the woman above the table shows her right hand up against her face, and her left arm folded, hand on the table. Her left arm doesn't appear to have moved, and there was no time for a transition from Pacey's knee to above the table. (00:00:55)
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.