Continuity mistake: In 'Graduation Day, Part 1' when Buffy and Faith are fighting Faith falls into a table, knocking all the comics on it onto the floor. In one or two later shots you can see (on the very edge of the screen) that there's still a comic on it.
Continuity mistake: In Graduation Day Part 1, when Faith and Buffy are fighting, Faith throws Buffy into the wall near the TV, but the TV is intact. A few shots later, there is debris on the floor, glass and such, from the TV, and when it's shown again, the TV is unbroken. This happens a few times. In Graduation Day Part 2, when Faith and Buffy are talking in the apartment, the TV is broken again.
Continuity mistake: In 'Graduation Day, Part 1' when Giles stabs the Mayor, as he takes the foil out of his chest you can see a wound on his shirt. When the shot changes it has disappeared. I know the Mayor is invincible and his wound heal in seconds, but it still takes a second or two for his wounds to close up, they don't just disappear.