Take me out to the ballgame - S2-E1
Continuity mistake: During breakfast, after Carrie and Sam check the newspaper, none of Miranda's movements are continuous: She swaps from using the fork to drinking to leaving the mug. Continuity mayhem.

Take me out to the ballgame - S2-E1
Continuity mistake: When Charlotte shows the newspaper to her friends it is wrinkled all over, but a shot later it is neatly folded.

Take me out to the ballgame - S2-E1
Continuity mistake: When Carrie picks the flyball Sam stands up and there's nothing in her right hand. A shot later a cup appears. Then it disappears again and a frame afterwards it appears next to the hot dog.

Take me out to the ballgame - S2-E1
Continuity mistake: At the stadium, when Sam orders a beer Carrie's leg is either on top of the chair or in between two chairs, depending on the angle.
Take me out to the ballgame - S2-E1
Continuity mistake: At the stadium Sam leaves her cup on the floor and stands-up to order beer. When she does so the cup reappears in her hand.

Continuity mistake: When Seth tells Carrie that Dr. G's plant is plastic his hand is either holding the glass or not. This changes back and forth.

Take me out to the ballgame - S2-E1
Continuity mistake: At the Yankees stadium, there's a man behind the girls buying food from a vendor. When the shot changes the vendor is gone and the man is already eating.
Continuity mistake: Carrie tells Seth that "Dr. G runs a psychological test" and Seth covers his mouth with his left hand. A shot later his hand is away.

Take me out to the ballgame - S2-E1
Continuity mistake: James walks towards the cab and kisses Sam goodbye, shot changes and he walks away backwards. Back to a shot on Sam and now check the reflection on the window below - James is now really close to the taxi and walking backwards again.

Continuity mistake: When Carrie talks about his first date with Seth there's an aerial shot of him holding a drink and taking a sip. A shot later he is not holding the glass.

Continuity mistake: When Stanford tells Carrie that she has to have a shrink, a man suddenly appears behind and the kid next to him changes positions between angles.
Continuity mistake: At the bar Sam drops her jacket on the floor and walks towards a guy. The jacket magically appears on the seat a shot later.

Continuity mistake: During the walk at night, after they cross the street and talk about "thinking delusional", a bunch of people appear out of nowhere between shots. (00:07:28)

Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: At the party, when the doctor leaves, Laurel holds the drink with her left hand but a shot later it's on her right hand.
Continuity mistake: While the girls walk down the street at night Miranda says "relationships are not about games" and the road behind is empty. A shot later in the close-up it's jammed with cars.

Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: Carrie and the doctor are dating for the day after and a waiter approaches on the left. A shot later he disappears.
Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: When Carrie meets the doctor there's a couch right behind them, plus a table next to him and another couch behind Carrie. A shot later they're surrounded by people despite the place being packed with stuff a second ago.

Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: When Carrie meets the doctor there's a waiter behind them who walks away towards Carrie's direction but suddenly disappears in the following shot.

Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: At the beach party, a fan meets Carrie who holds her beer with both hands or one depending on the angle.

Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: When Samantha meets the doctor at the beach her legs are crossed or not depending on the angle.
Answer: I'm a long-time fan of the show, having re-watched it many times, and I definitely remember slightly different dialogue at the end of that episode than what's on my DVD. I'm afraid I have no idea why this change might have been made or any other info, but you're not insane.
Purple_Girl