Visible crew/equipment: When Joey is walking out to the pier to talk to Dawson, right after the wedding; the wind is blowing her dress back and you can see a prominent, solid line going up the front of her dress from about the waist up to the neck. I assume this is probably a microphone wire of some kind and not just a wrinkle, as the line is solid and protruding through the material.
Revealing mistake: During this scene Joey is running from the wedding to find Pacey. There is a young couple dressed in light blue, standing on the left side of the scene. The man appears to turn his head and see Katie Holmes running towards them, and puts his arm around the woman next to him and directs her across the grass over to the right. They both sort of suddenly run over to the right in order to clear the way for Katie to keep running straight through the area. It's obvious they moved intentionally so as to get out of her way, knowing the actress was about to run by them.
Factual error: When Joey is driving the light blue pick-up truck, Doug pulls her over to tell her Pacey is leaving town. Right before she pulls over, in her close-up there is a sticker on the lower corner of the driver's side windshield, which looks like it could be the North Carolina State Safety Inspection sticker (small square decal with a yellow emblem in the center, and blue writing along the top and down both sides of the decal), as opposed to a Massachusetts inspection sticker (which would be on the passenger side).
Continuity mistake: At the very end of the episode, when Joey and Pacey are sailing out into the sunset the sky keeps changing between shots. When they are first setting off, it's earlier in the day with bright sun and a cloudless sky. The sun appears at a high angle. The next shot, as they sail further the sky is suddenly full of clouds and it's almost sunset, with the sun lower in the sky. The final shot after that, the sky is still cloudy and in sunset hues as the sun appears just over the horizon about to set. Obviously these shots were taken at different times of the day, although they appear to be right after each other in the show.
Plot hole: During this ending scene, Joey runs frantically to find Pacey and asks to go with him on his sailing trip all Summer. She is carrying absolutely nothing with her, not even a purse or wallet. Her pockets are completely flat, and she doesn't even appear to have ID. Joey's lack of luggage or clothing is explained in her dialogue, as she jokes about the next change of clothing. She probably assumed she could buy what she needed along the way, and was in a hurry not to miss Pacey's departure. But it doesn't seem logical that she would take off for an entire Summer without any type of purse, wallet, money, credit cards, ID, etc. as she would have no way to pay for anything. She would also need her ID in order to work the odd jobs she mentions in Season 4.