Twenty-something girls vs. thirty-something women - S2-E17
Deliberate mistake: In the scene at the beach party, when Carrie brings everyone beers, Miranda says "There's so much foam, I could ski on the head," but the cups are tipped toward camera and you can see there's no foam at all.
Deliberate mistake: Coming back to Earth in 1998, Stone is amazed to see the Cincinnati Reds and the NY Yankees on TV in an interleague game. This wasn't yet possible in '98, as an American League East team could then play only a National League East team (and the Reds are NL Central). But the producers put it in anyway as their own little "fantasy baseball game," because these were their favorite teams.
Pilot (aka Emotions in Motion) - S1-E1
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)
Wrestling with Demons - S3-E12
Deliberate mistake: When Piper froze the demons (near the wrestling) one of the demons moved when she froze him.
Deliberate mistake: At the beginning of the episode, when Doug and Carrie are in the shower, you see their silhouettes. The first mistake is that for the silhouettes to show like that they have to be evenly backlit which wouldn't make sense in the shower. The second mistake is a little more subtle; you can see the outline where the actor's bathing suits are (inevitably) slightly larger than the bodies. There is also a slight darkening in the areas where the bathing suits cover skin. (both of these things are much easier to see on Carrie than Doug because of her smoother figure and skin tone).
Winning Through Intimidation - S1-E15
Deliberate mistake: In the actual card game, attacking the castle ring would not be allowed, but this is probably done in order to enhance the show for kids.
Formidable Enemy!? Mother Coordinator Enters! - S7-E37
Deliberate mistake: This Pokémon Trainer's Choice segment incorrectly claims that Arbok evolves into Seviper, which isn't true. (00:11:38)