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: In the one where Joey and Chandler lose baby Ben on a transit city bus, they later have to pick him up at the transit city headquarters. The man working there assumes that one of them is the father. There is no way that a city official would just give away a baby without checking for ID or a birth certificate or proof of fathership of the child.