Revealing mistake: Towards the end of this episode, Joey comes back to her Dorm room and spots the envelope Eddie left for her. You can see her name written on the outside of the envelope, and it's supposed to be Eddie's handwriting. But in fact, it looks exactly like Joey's handwriting as shown throughout the series. When Joey is talking earlier to Professor Hetson and he hands her the exam booklet with her writing on the front, it's the same style of handwriting. During other episodes, we see what is supposed to be Joey's own writing (ie: her note to Dawson during the Series Finale that she leaves on his bed) which is also very similar. So in fact, what is supposed to be Eddie's handwriting on the note to Joey really looks more like Joey's handwriting, or the same person who really does the writing for Joey's character.
Revealing mistake: When Pacey and Rich are physically fighting in the office, there is a quick shot of a person who is supposed to be Pacey leaning forward over Rich and hitting him. However, if you look closely you can see that the hair on this person although dark brown, appears much longer and curlier than Pacey's current hairstyle. Also-just before that shot ends, you can see the longer hair swing away from his neck loosely on the right side. The next shot of Pacey shows his shorter haircut, so I believe the longer hair was actually a stunt man substituting for Pacey in a risky, physical scene. (00:40:00)
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.