The One With The Dirty Girl - S4-E6
Other mistake: When Rachel tells Joey he can't get Kathy another "coupon for an hour of Joey love", you can see Chandler (Matthew Perry) mouthing the words "Joey love". (00:17:21)
The One With The Fake Party - S4-E16
Factual error: Phoebe says in the show that she's three months pregnant. Not only is she way too big for that, but the fetus also kicks for the first time. Women don't feel fetal movement until 16 weeks at the earliest, and for a first pregnancy it may not be until 25 weeks or so.
Suggested correction: Phoebe's size could partially be explained in that she was carrying triplets, though Lisa Kudrow was pregnant in real life, and was further along than her character. Her pregnancy had to be written into the show and the gestation timelines did not match up. Phoebe feeling "movement" could just be her imagination, as her character is supposedly somewhat psychic and often perceives things that are not necessarily discernible to others or isn't even real.
The One With Joey's New Girlfriend - S4-E5
Continuity mistake: When Ross goes to Amanda's house for a date you see her two children sitting on the couch. The little boy with blonde hair is sitting down, when it cuts to Ross and Amanda talking the boy is standing up on the couch, the next shot he's sat down as Amanda walks out the door.
The One With The Ballroom Dancing - S4-E4
Visible crew/equipment: When Phoebe and Rick are sat on the massage table, keep an eye behind Phoebe's head when the camera is on her, particularly after Rick says, "I can always find another masseuse." You can see the shadow of the boom mic moving.
The One With Phoebe's Uterus - S4-E11
Continuity mistake: In the scene where Joey is showing kids around the museum, there's a little boy who corrects Joey about the existence of the Mastodon. The kid's arm is by his side at the beginning of the scene. When he begins saying, "Isn't the Mastodon from the Pliocene Epoch?" his left arm is suddenly up and his thumb pointing at the Mastodon. (00:07:05)