Plot hole: When Buffy enters the house to rescue her mother she uses a stake to stop the front door from closing. A vampire then grabs it and the door closes. Why did Buffy use a stake knowing that there was a vampire there when she was almost killed by a vampire with her own stake earlier in the episode because Giles had been injecting her with a muscle relaxant?
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.
Plot hole: After losing his soul, Angelus kills Jenny Calender's uncle, who is a descendant of the gypsy clan who cursed him. But, since there is nothing to suggest the uncle's room is in a public location, Angelus couldn't have gotten in the room without an invitation.
Life Serial - S6-E5
Plot hole: In the 3rd time loop at the magic shop, the woman looking for the mummy hand looks surprised when Buffy knows what she wants. In the 2nd time loop, the woman tells Buffy that she called the shop 20 minutes earlier and was told that they had one. Therefore at least one of the shop's staff would be aware that a woman would be arriving looking for a mummy hand.
Plot hole: Willow hacks into The Initiative's computer system and discovers air ducts and electrical conduits leading to Adam behind 314, but the room doesn't show up on the schematic. It seems unlikely that nobody who didn't know about Adam would have noticed this and investigated.
Plot hole: Healing Angel requires draining the blood of a Slayer. Buffy tries to kill Faith in order to get some of her blood but Faith gets away after Buffy stabs her at the end of "Graduation Day Part 1." The amount of blood on the dagger that she used wouldn't be enough blood to heal Angel, but it'd be a start. So why didn't Buffy just use some of the blood on the dagger? In the very first shot of "Graduation Day Part 2" we see the dagger coated with the stuff.
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).
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.
Chosen answer: He had larangitis and because of the shooting specifications they had to have him shoot the scene with a bad throat, they then re-recorded his lines and dubbed them. At various points during the scene and indeed the episode you can see him touch his throat or rub it.