Continuity mistake: Towards the end of the episode, Ross and Chandler come into Monica's apartment and Ross asks where Rachel is. Watch the objects in Monica's hands, in the shot from behind she puts them on the table, and then does it again in the shot from the front.
Continuity mistake: When Rachel and Phoebe are talking in the Baby Beauty Contest and Rachel is holding Emma, Emma's head instantly changes position between shots several times, often going through 180 degrees. Clearly they couldn't get her to do the scene in one take and therefore the editing suffers.
Continuity mistake: Ross claims he looks into Monica and Chandler's and watches them eating dinner and watching TV. His apartment is a floor lower down than theirs and with the balcony wall, the sofa and tables distance from the window and the fact the bottom of the window is higher than the floor, there is no way Ross would be able to see that far in. We have seen in the past that he can basically only see who is at the window.
Continuity mistake: When Monica comes round to Phoebe's, Phoebe reminds her that she's got to clear out stuff. In this wide shot Monica has both hands by her sides, but when it cuts to her finishing saying "oh right", her right hand is now gripping her bag's strap.