Continuity mistake: After drinking the water with the virus, Buffy looks into a room and her hair is damp and brushed back. In the next shot, it's dry and parted down the middle.
Once More, With Feeling - S6-E7
Revealing mistake: When Buffy is singing in the Bronze with Anya and Tara as backup you can see Tara bump into the pillar and then dust herself off. (00:41:45)
Visible crew/equipment: While Xander tells the gang about the "demon" he encountered, they all walk into Giles' apartment, and just as Xander heads up the stairs, the white T-mark taped to the rug is visible under the corner of the desk with the lamp, where Willow will stand. (00:27:00)
Plot hole: Angel says he cannot give Buffy mouth-to-mouth because vampires have "no breath." However, throughout the entire series, vampires are shown to breathe, and are able to do things like smoke, gasp, get choked out, etc. (Granted, the franchise also confirms a vampire cannot die from asphyxiation, but still they're shown to breathe regularly).
Other mistake: In the very first shot (a long tracking shot backstage), watch the girl practising with her tuba. At one point she pulls her mouth away and then leans back in and starts playing some notes. But you can tell that she isn't blowing into it, and in fact, her mouth isn't even quite touching it. So it shouldn't be producing any notes. Then, almost immediately after, you can also see the actress purposely moving the tuba (sort-of rotating it to her right) to get out of the cameraman's way.
Factual error: When Willow is chatting with "Malcolm," she says she has to sign off the chat program after she gets nervous. However, all she does to "sign off" of the chat program is turn off the computer monitor. This would do literally nothing. The program would still be running if you turned the monitor back on. Yet the episode treats it like she's just turned the entire computer off by turning off the monitor.
Continuity mistake: Anya's hair changes from straight in the previous episode to curled in this one, even though it is set directly after.
Nightmares - S1-E10
Continuity mistake: Buffy's history teacher is not the same person from episode 1 or 9, originally a woman, the teacher is now a man. Cordelia also notes Buffy doesn't know where the class is due to ditching, but we saw Buffy in her history class with Cordelia in The Puppet Show. How could Buffy not know where her class is only 1-2 weeks later?
Other mistake: Buffy freaks out when she's first taken to the hospital. Joyce tells the gang it was because her cousin died when they were young, but in season one episode "Angel" Buffy has no problem being in the hospital, same with later seasons.
Continuity mistake: In the end of the scene where they find the dead mental patient killed by the meteor alien, the group walk away from The Body leaving Riley still there, but Anya's coat can be seen in the bottom left corner after she had walked away.
Visible crew/equipment: When Willow does her spell to save Tara, you can see the black pad Tara falls/ stands on.
Visible crew/equipment: In the final scene with Anya and D'Hoffryn the edge of the backdrop (and the set behind it) is visible when D'Hoffryn walks around her. (00:40:10)
Dead Things - S6-E13
Revealing mistake: In "Dead Things," after Buffy and Spike sleep together, when Spike asks, "Are we having a conversation?" and Buffy says, "What? No?" There is a side shot of her. If you look closely at her back (pausing helps), you can just barely see Buffy's skin colored tube top. Trust me, it's there. The time code is 1:22.
Continuity mistake: After Riley stakes Spike and Spike decides to drink, he is shown opening the bottle. The camera shows Riley and then goes back to Spike. Spike is holding the bottle, lid still on, then he goes to open it again.
Revealing mistake: In the scene when Oz stops the female wolf from attacking Willow, and they both change and Oz tears her neck out, if you look closely, you can see the actor's real skin at the neck.
Visible crew/equipment: While Buffy, Giles, and the gang are in the library fighting the demon that came out of the Hellmouth, the camera zooms toward the door that leads into the hall, where you can see Xander being chased by the dead guys. As the camera zooms in closer towards the round window in the door, you can see its reflection in the glass when the strobe light flashes. (00:36:10)
Welcome To The Hellmouth (1) - S1-E1
Plot hole: There was no need for the master wait 60 years for the night of the Harvest, when all he had to do was have his minions kidnap and gather a bunch of humans and bring them down to where he is so he could feed on them himself and escape 60 years earlier.
Character mistake: Giles picks up the potential slayer Chao-Ahn from Shanghai in Episode 7.12, "Potential". However, when she arrives in Sunnydale (Episode 7.14, "First Date"), the language she speaks is neither Mandarin nor Shanghainese (the two main languages spoken in Shanghai), but Cantonese, which is not widely spoken there. (00:08:55)
Chosen answer: Angel is saying that he is still jealous and Buffy recognizes that this is his way of saying he wishes that they could be together. That is why they both smile.