Other mistake: In the scene near the end when Faith is putting Joyce's lipstick on in the mirror and taunting her, it is obvious that the make-up department forgot to put Faith's tattoo on her upper arm. It's obvious if you watch back and forth between the mirror and the shot of Faith standing and turning, there is no evidence of a tattoo that has been established Faith has in the previous season.
Other 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.
Continuity mistake: When Glory challenges Dawn to name one person who can cope with life on earth, there is a close up of Dawn answering "Buffy". In this shot, the black mark (where she has been annointed) that is there before and after, has completely disappeared.
Continuity mistake: Near the start of 'The Wish', the scene where Cordelia is talking to the Cordettes and meets Anya. During the close-ups of Harmony, Anya is standing to camera right of the brunette Cordette behind her. A few seconds later when the shot is further away Anya is standing camera left of the Cordette.
Visible crew/equipment: After Tara is found in the Janitor's closet and brought back to her room as Willow & Buffy come in, there is a mirror to the left of the door. It has a scarf draped over it to prevent it from reflecting things it shouldn't, but the bottom right corner is still exposed and in it you can see glimpses of the crew moving around behind the camera.
Factual error: After Buffy drags Xander down to the basement she locks the door and goes upstairs to find Dawn. When she locks the basement door, the handle is on the left side of the door and she turns the key to the right. In reality, a door with the handle on the left needs the key to be turned to the left to lock it. So Buffy did in fact unlock the door, not lock it.
Visible crew/equipment: When Buffy, Willow, Xander and Giles all agree that Morgan is their one suspect, a camera and a cameraman can be seen in the reflection of the glass in the door labeled "Librarian", right after Buffy says, "Uh, priority check, Giles." A boom mic is also reflected in the top right of the glass when Buffy finishes her line with "talent show murder!" The mic can be seen throughout the rest of the scene from two different camera angles.