Continuity mistake: Rachel is talking to Joey in his apartment after waking up the next morning, looking messy and rumpled. As she talks, her bra strap slips down her arm. In one shot (as she says "I'm a horrible person"), the strap is all the way down her arm and then in the next shot it is tucked under her shirt.
Visible crew/equipment: After Jill comes to Monica's apartment, they are all around the table in the living room. As the camera is moving from Jill, to Monica and Chandler, who are sitting on the couch, a camera-man is visible in the kitchen behind them, complete with camera and trailing wires.
Continuity mistake: Just before Chandler gives Monica the mixed tape, he tries to manipulate a coat hanger into something feasible. He stretches it out and holds it up, saying "Yes, honey, I made it myself," then the camera cuts to another angle as he throws it down. After the cut the hanger is not as stretched as it was before.
Visible crew/equipment: In the scene where Phoebe knocks over the vase, after she says, "Well, that's just the way things go" and turns around to face the babies again, you can see a crew member coming out of Rachel's room. When Phoebe starts looking for the missing baby, the shadow of the crew member is visible on the right of the screen as the baby is placed in the drawer.