Deliberate mistake: Though vampires are said to possess super-human strength, and are in fact demonstrated to have it, they are often kept confined by the flimsiest of restraints. One distinct example is in season 2 episode 9 when Kendra locks up Angel he is unable to break out despite being held in by nothing but a flimsy padlock. This mistake is pointed out in the DVD commentary as an unavoidable 'mistake'.
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Continuity mistake: When we see Xander and Anya going over the seating arrangements for their wedding, Xander is eating from a large sack of crisps. During the conversation Anya takes them off him, he takes them back and places the bag next to him. We see the bag after Xander puts it down, and in a closeup shot of him, the front of the bag is facing upwards. But when Dawn comes in, the front of the bag is facing downwards - barcode and ingredients are visible.
Continuity mistake: At the beginning of the episode when Buffy offers Dawn another burger from Doublemeat Palace, she is holding the burger in her hands just before Willow comes in with her line, "Hey, workin' lady. Rough night?" The burger then jumps from the kitchen counter to Buffy's hands between shots.
Continuity mistake: When Buffy and Spike (as Joan and Randy) are fighting Bro'os vampires, Buffy kicks down a post box to stake one of them. The pole supporting the post box breaks away at a jagged angle. But when she uses it to stake one of the vampires the end that she uses has suddenly changed to the traditional triangular point, only to return to its original jagged angle immediately afterwards. The shot of her staking the vampire is not a side angle of some uneven ends. Watch as she backs away from the vampire after he's been staked, it is a fully triangular point.
Continuity mistake: When Oz turns back into a werewolf, he chases after Tera. She hits him with a chair and he falls to the ground and passes out. We then see The Initiative show up and learn that Riley has shot Oz with a dart (it's sticking out of Oz's side). But two shots earlier the dart wasn't there.
Continuity mistake: When Oz shows up at Buffy and Willow's dormitory, Willow has a lump or a pimple above the left corner of her mouth. It disappears later in the episode when she's talking to Buffy about her feelings for Tara and it returns at the end when she and Oz are in his van.
Audio problem: In the episode 'Once More, With Feeling', when Anya sings her first few lines of the song 'I'll Never Tell', you can still hear Xander talking about omelettes in the background, but for the last few lines he speaks (from 'I could do an omelette' onwards) you can see over her shoulder that his voice is dubbed.