Continuity mistake: When Pacey drives Joey and Dawson to the market to get party supplies, they leave in broad daylight. It can't be more than a few minutes down the road, being such a small town. Yet as they drive there, the sun is suddenly going down, and when they arrive at the store it's dark and night time. It couldn't have gone from broad daylight to dark night time in that short period of time. It appears to be a very long drive, but it's just the local market.
Plot hole: When Pacey drives them all to the market, he explains that he had to 'steal' the car from his family, and thus doesn't have the keys. He makes Joey stay in the car while they are shopping, because he can't turn off the car. But later, at the end of the episode, Pacey suddenly goes running out of Dawson's house late at night, jumps into the same car and turns keys in the ignition to start it and drive off in a hurry. How would he suddenly have the keys to the car? He drove them all straight to Dawson's house from the market, with the crazy girl - and the car had been there ever since. He had no time to go back home to get the keys; and it isn't likely his father, the town sheriff, would allow his underage son without a legal driver's license, to have the keys.
Deliberate mistake: Throughout the first episode, Jen's bangs are long in scenes relating to her "Grams" and short in all other scenes. This is because the scenes involving her storyline with Grams was shot much later, after the show was picked up. (00:05:45 - 00:16:15)
Visible crew/equipment: It's morning at Jen's and Grams'. Jen is seated at the kitchen table downstage/far left. Grams is upstage/right at the stove scrambling eggs. Grams crosses downstage to put the eggs in front of Jen and the mic overhead upstage/right peeks out just a tiny bit. Grams crosses back to the stove. Suddenly the microphone - including the rod the mic is on - just drops down almost completely into the frame over Grams' head and is not pulled back up.
Continuity mistake: After Joey finds the visitor Anderson playing a violin on his yacht, they have a back and forth conversation where she hides her work apron behind her back. When the camera angle switches back and forth, her arms are in different positions. (00:14:10)
Other mistake: After Dawson and Jen order "cokes" from Joey at the seaside restaurant, Joey pours their drinks into plastic red cups. She only pours several milliliters of cola into the cups, barely enough for one gulp. (00:29:50)