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.
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.