As Giles fumblingly attempts to ask Jenny out, an Asian girl with glasses and a black miniskirt comes out of the door in the background. As Jenny is leaving the scene, the same girl comes out of the same door again.
Buffy says "whoever was buried here" despite being face-to-face with the grave's headstone, which would have clearly stated a name, birthday, and death.
The premise of the plot is that Chris and Eric are looking for a "viable head", despite there not being a single case of a successful head transplant in the history of medicine to date. Of course, vampires do not actually exist either, so allowances have to be made, artistic license to create highly watchable story-line.
After cheerleading practice, in a suspenseful scene on the parking lot, Cordelia drops her keys when frantically trying to get into her car. In the next shot, the keys are suddenly more than a full arm's length under the car. This is impossible because it was shown they just dropped straight down and she didn't kick them or anything.
(at around 36 mins) As the cheerleaders cheer at the game, you hear them quickly say "Go, Razorbacks, Go!" The Sunnydale mascot is the Razorback, but the subtitles on the DVD say "Greenbacks."
Angel mentions he's 241 years old. That would mean he was born in 1756. This is discovered to be incorrect in "Prodigal" (Angel, s1e15) - it's seen there that Angel was born in 1727, making him about 270 years old here. It's possible he's regarding his age from when he was sired and not when he was actually born, but that would also be incorrect since it's also learned in "prodigal" that he was sired in 1753, which would make him 244 years old.