Continuity mistake: When the female watcher is being destroyed after Buffy cuts off her arm. Her sleeve is empty, which is not possible, as Buffy could not have removed the arm but not the sleeve. Also the arm on the floor is removed at the elbow, but the watcher has lost the entire arm in a previous shot.
Revealing mistake: When Gwendolyn Post fights Angel in the mansion, she breaks a long-handled shovel over her knee to create a stake. If you watch in slow motion, the handle of the shovel is pre-broken (she simply holds the two pieces together tightly), and the pieces separate just before they actually make contact with her knee.
Deliberate mistake: In the fighting scene, the glove of Myhnegon is used by the new watcher who directs it toward the ceiling of Angel's living quarters where there is a huge skylight. The skylight is not seen in any other episode and its presence would have burned him on other occasions.