Plot hole: In TOW Ross tells Rachel he cannot see her following a promise to Emily, the rest of the friends go into Monica's bedroom. Joey hauls out a box from under the bed, saying that he's been hiding it there since Ross said the wrong name at the wedding. Surely Monica, with her obsession for keeping the place clean, would have noticed a box under her bed?
Continuity mistake: Just after Rachel throws a bread roll at Joey, he turns to Chandler to speak to him. Chandler is holding his hands out in front of him. In the next shot, his right hand is touching his face, then in the next shot, it is lowered again.
Continuity mistake: In this episode, Rachel tells Chandler that she thought he was gay until he spent Phoebe's entire birthday party talking to her breasts. But at this point since Rachel joined the group, Phoebe hasn't had a birthday yet; that occurs some episodes later, in "The One With Two Parts."
Plot hole: Chandler has always loaned Joey money for various things (rent, acting classes, Christmas gifts, etc), so he shouldn't be surprised to learn that Joey doesn't have money for fancy dinners or birthday celebrations. Plus, Joey never seems to have a problem taking money/handouts from Chandler - why now? Also, Chandler explains that they're buying Ross a cake ($20), but why doesn't Monica (the chef and his sister) just make him one?
Other mistake: When Ross is helping choose a dress and shoes for Nana to wear, he is behind the chest of drawers in the cupboard. He looks in a shoebox and finds lots of pink sweet'n low packets, then pulls down another box and lots of packets fall down on him. However, it is obvious that someone is above him showering the packets down, as they are coming from directly above him, not from on top of the door.