Visible crew/equipment: When Ben arrives in his car and discovers the Knights of Byzantium, the shadow of a camera on a crane can be seen in the bottom left corner of the screen as he pulls up.
Revealing mistake: Near the end when the good Willow says goodbye to the evil Willow and hugs her, there is a shot of the back of the good Willow's head and the evil Willow's face. You can tell that the good Willow is a body double wearing a wig - there's something circular near her scalp, possibly an elastic band.
Audio problem: Jenny prints off the translation for the Ritual of Restoration from her computer, then spots Angel sitting across the room from her. As she gets up and starts walking towards him the sound of the printer can be heard but the paper has already finished printing.
Revealing mistake: When Jonathan assists Buffy at the beginning of the episode, he enters through the glass ceiling of the mausoleum, which shatters into squares. Although the audio is the sound of glass shattering, the pieces of "glass" flutter down, revealing that the squares are paper - simply for the safety of the actor during the stunt. (00:05:00)
Once More, With Feeling - S6-E7
Audio problem: In the final song "Where Do We Go From Here", you can hear Spike still singing even after he has apparently stopped. He and Buffy continue singing until after the line 'When do the trumpets cheer'. It is noticeable because James Marsters sings the word 'cheer' slightly out of sync with everyone else.
Continuity mistake: When Buffy is being offered the 'doublemeat medley' burger by her boss, the burger looks different in close up than in the long shots. In the close shot, the burger looks overall bigger, more filling is visible and there is more lettuce sticking out.
Continuity mistake: Just before Buffy storms out on Spike, she puts on her denim jacket. When viewed from in front we can see the jacket is only half over her shoulders and her hair is loose. The shot cuts to view her from behind, and the jacket is now completely on and her hair is tucked under the collar.
Continuity mistake: The first shot of Maggie Walsh being impaled from behind with the skewer indicates that there is no one standing close by, judging by the amount of negative space around her. However, following shots reveal that the skewer is coming straight out of Adam's wrist, therefore he should have been visible in the previous shot.
Plot hole: In the flashback to Buffy in L.A., how did Angel get there with the front windshield of his car blacked out? Being a vampire, he obviously needs it during the day, but he also wouldn't be able to see traffic. And it just seems to be too much of hassle for him to remove it at sunset, just to reapply it at sunrise, just to remove it again, etc.
Continuity mistake: In 'Graduation Day, Part 1' when Giles stabs the Mayor, as he takes the foil out of his chest you can see a wound on his shirt. When the shot changes it has disappeared. I know the Mayor is invincible and his wound heal in seconds, but it still takes a second or two for his wounds to close up, they don't just disappear. (00:15:40)
Once More, With Feeling - S6-E7
Revealing mistake: The knives Giles throws during Buffy's training are a very poor CGI job if you watch it in slow mo. All three knives Giles takes off the wall are identical, with a broad curved blade and a plain black handle. The first one has a transparent blade as it flies toward Buffy, then we hear it bounce off the far wall and it's way out of scale for the distance. The second knife has a diamond-patterned grip instead of a plain one. The third knife conveniently spins in midair for a second so Buffy can kick it out of the way. (00:30:35)
Continuity mistake: The finger changes position in Buffy's hand as she picks it up. (00:23:35)
Revealing mistake: Towards the end, when Buffy stabs Faith, there is no blood whatsoever.
Revealing mistake: When Buffy breaks into the locker, the locker is already damaged. Probably from a previous take.
Suggested correction: Watching the scene, the only real damage is a slight dent that isn't all that close to the lock (she basically punches out the lock to open it). And to be perfectly honest, a dented locker isn't out of the ordinary for a high school. I saw plenty of dented, bent and damaged locker doors all the time back in high school. It's entirely probable that it is damaged from a previous take, but I think it's also within that sort-of realm of possibility (since like I said, dented lockers aren't out of the ordinary) that it might not be considered a mistake. I'll leave it up to people's votes.