Visible crew/equipment: In the opening shot of Phoebe and Chandler in the "nine millionth" jewelry store looking for a ring, at the top of the screen we can see the tip of the boom mic moving in the wideshot. Then just as Chandler looks into the display case and says, "Ugly ring. Ugly ring. Ugly ring," the boom microphone can be seen moving around in the mirror's reflection behind him.
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Plot hole: When Phoebe accidentally allows Chandler's ring to be sold, she tells him that she overheard which restaurant the guy said he was taking his girlfriend to, so they can go find him and persuade him to exchange rings. However, in the previous scene we see that Phoebe was paying no attention at all to that guy - she was too busy trying on jewellery. She wasn't even within earshot of the guy, and we see from her reaction that she hadn't even noticed him at all before he left the store with the ring (during which time he doesn't say anything at all).
Continuity mistake: Paul finally opens up, and cries like a baby to Rachel. While talking to her at the breakfast bar in the kitchen (when Rachel is trying to distract him with sex), he's wearing a white linen shirt that constantly changes between tear-stained and wrinkled to ironed and clean.
Plot hole: In the opening scene Phoebe and Chandler discuss how Phoebe knows Chandler is going to propose: by walking in on him whilst he was looking at a ring catalogue on the toilet. However, in the previous episode Chandler leaves the apartment right after he found out about Monica booking the wedding slot (on the answerphone) and doesn't come back until he 'freaks out' at Monica and then it is revealed that it was just put on and Phoebe is in on the plan. It doesn't add up, as Chandler would have had to have been looking at the catalogue between hearing the message and deciding to propose, in the same afternoon when he wasn't even in the apartment.