Continuity mistake: Near the end when Monica and Chandler are going on to dance for the last time, Monica speaks and her hair is neatly behind her right ear. The shot then looks to Chandler before going back to Monica immediately. However her hair is suddenly behind her left ear when she can't have moved it as her hands are in the shot at all times. (00:21:15)
Other mistake: When Chandler says "We just got married. Right there!" and points. We hear a small 'ding' and Monica asks "Is that your ring?" But when Chandler pointed, you can see that all of his fingers except his index finger are closed to his hand. So the ring couldn't have come off. (00:00:05)
Plot hole: Chandler and Ross are surprised to notice that Joey has very small feet. It's well beyond suspension of disbelief to think that at the least Chandler (who, apart from being his best friend, has been his roommate for 8 years) has never noticed the size of Joey's feet before. (00:11:20)
Other mistake: In "TOW the cheap wedding dress" the whole episode is about how Chandler wants "The Swing Kings" to play at the wedding, because, at their concert, that is where he realised that Monica was the woman he wanted to dance all his dances with, and Monica goes to great lengths to secure the band. In this episode, the band at the wedding is actually called "Jungle Swing".