Revealing mistake: The entire scene where Buffy is experiencing accelerated time, shadows of trees move in the wind but never actually grow or shrink. Even over short increments of time, the sun can move shadows noticeably, and judging from the speed of the people around her, Buffy is in accelerated time for at least half an hour.
Factual error: When Buffy and Angel escape from Spike, Dru and the Judge they jump down into the sewer, then run all of five metres before going up the ladder to escape. When they come out of the sewer they are in a very open area with the factory nowhere in sight. They have not travelled far enough for this to be the case.
Continuity mistake: When Buffy is giving her speech about being chosen, there is a shot of Andrew sitting on the couch next to Xander and Anya, but in several of the shots of the Potentials he can be seen standing on the other side of the room in front of the curtains. It's definitely him - his face isn't visible, but the clothes are the exact same.
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.
Revealing mistake: When Buffy is fighting the vampires that are trying to resurrect The Master, at one point she is grabbed from behind by a male vampire and kicks a female vampire in a green top twice (right after Absalom shouts "The sacrifices! Stop them!"). If you watch closely, both of the kicks miss the vampire, revealing that the fight was choreographed. The punch that she delivers to the male vampire afterwards also looks fake.