Continuity mistake: In the one where Ross finds out he's having a boy (series 1), just before Rachel lets it slip, she is sitting on the edge of a chair eating a cookie. Watch her dress, it changes back and forth from being undone from the waist up, to only having two buttons open at the top.
Continuity mistake: In the scene where Monica is explaining to Rachel that she has hired her friend Wendy as her waitress, Rachel is holding a water bottle in one hand and the cap in the other. Monica moves towards her and Rachel is pointing her hand in Monica's direction and then in the next shot we see Rachel from another angle and her hand is holding the cap on top of the bottle too fast to have happened in normal time.
Continuity mistake: When Stephanie is singing "Angel in the Morning", there is a person in overalls sitting behind the green pole. The shot changes to Phoebe outside and you can still see the person; it changes back to Stephanie and the person is now sitting on the next table.
Factual error: Joey always grabs his back when he gets his pain from his kidney stones. This is a classic referral pattern for pain when the stones are in the kidney. However, the doctor says that the kidney stones were too close to the bladder. Stones in the ureters classically refers the pain to the groin area.
Continuity mistake: When Joey is interviewing the potential roommate and Chandler comes in, Joey's stance changes a few times. His grip on the application form changes, and when he points to the bathroom his arm is in a slightly, but noticeably, different place in the next shot.
Visible crew/equipment: When Monica, Ross, Chandler and Rachel are at the apartment and Rachel is suggesting how funny Chandler is, as soon as Ross says, "Sweetie, calm down it's going to be OK," a boom mic can be seen for a short period of time, at the top of the screen.
Continuity mistake: When Ross and Rachel argue about losing Marcel, the bottle of wine Ross re-corks is sitting on the table. Neither of them touch the bottle at any point after this yet when the woman from animal control arrives, the bottle has moved to the side table.
Continuity mistake: In the scene where Monica and Ross discuss how Emily has decided to call off the wedding after Monica suggests they postpone the wedding, Monica is wearing a black watch on her left wrist. This disappears and re-appears a number of times throughout the scene.