Continuity mistake: When Willow hides under the table in the classroom after fleeing the pack, we see that it is on legs and doesn't touch the floor. Yet when Xander comes in and scans the room, he sees the table but Willow's feet aren't visible, even though they should be judging by the height of the table from the floor.
Continuity mistake: When Buffy is told that Angel has become Angelus, she mentions "I should have known. When I saw him at the house he was different", but her earlier conversation with him took place not at the house but at his apartment. This isn't just a strange turn of phrase - the scene was originally shot at the Summers house, but was changed to Angel's apartment for more emotional resonance.
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: In 'The Initiative', Riley, Graham and Forrest are looking in through the windows of Stevenson Hall with thermal goggles looking for Spike, they see him walking towards Willow. When we see Willow and Spike seconds later he is still sitting on the bed where he was for most of the scene.
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.