The drawing on Dawn's easel after she learns of Joyce's death is not the same one she had earlier. The original drawing had large black areas and the new one shows those areas much lighter.
In the art room, when the scene cuts between Dawn and Kevin, Dawn's drawing is different each time.
Paramedics in the state of California are not allowed to pronounce death. Joyce would have been taken to the hospital where it is likely she would have been pronounced DOA. Also, once paramedics begin CPR, it is usually not allowed to be stopped until someone with a higher degree of medical training takes over.
On the closeup after Buffy vomits on the carpet, the makeup used to make Sarah Michelle Gellar's face look pale is clearly visible on her lips, as it leaves an evident line.
Corpses are stripped in morgues but in several shots the underwear of the vampire attacking Dawn and Buffy is visible.
(at around 30 mins) When Xander and Anya are walking along the hallway to Willow's dorm room, as they pass an open door, the viewer can see that there is no room and the scaffolding of another set through the doorway.
When the doctor comes to speak with the family, the camera follows Buffy, Dawn and Giles as they go to meet him, and there is a moment at 32:13 as they pass out of frame when you can see a pair of "marks" on the carpet at the bottom left of the picture, one made of white tape and the other of red. Later, when the doctor and Giles leave and the rest of the Scoobies come over to join Buffy and Dawn, Xander hits the white mark and Willow the red one.
(at around 41 mins) After they sit down, a camera is visible on the wide screen on the left.
At 06:30 as the camera zooms on Buffy's face, the wide screen shot shows what is probably a mike, in the top right corner.
When the paramedics are doing CPR, the one who is supposed to be doing chest compressions is pushing on Joyce's stomach, not her chest.