At about 36:40 when Buffy and Giles are up by the stacks talking, you can see the placard that says "601-800", and it is perfectly fine. Then Buffy walks down to the table where everyone else is and starts talking. The camera switches back to Giles at the stacks and the placard is pushed out about half way.
In the opening scene set in Angel's home city of Galway, Ireland, crickets can be heard chirping - however, Ireland does not have such nighttime crickets as the climate is too cold. This is false information. A quick search on the World Wide Web establishes that Ireland does have nocturnal insects that make chirping sounds. It might be that the contributor became confused by snakes. There are no snakes in Ireland because it is just too cold for them to live there.
The flashback to Angel's introduction to Darla in Galway, Ireland establishes that it's 1753. Canon establishes that Angel is 241 years older than Buffy in 1997. Either he hadn't been born or, even if vampires count their age from the year they're "made", the numbers simply don't add up.
At thirty-two minutes in, as Buffy fights her first-ever vampire, in the distance you can plainly see a portable lighting mast on the far side of the cemetery wall. Atop it (just out of frame at the top of the picture) are the instruments supplying the "moonlight" which illuminates much of the scene and serves as a strong back-light for the actors.
As Kendra and Drusilla are fighting, a black lighting flag is occasionally visible at the top edge of the picture.
The L.A. cemetery where Buffy fights her first vampire in 1996 bears a striking resemblance to the 1998 Sunnydale cemetery where she kills two vamps at the beginning and fights Angelus toward the end. Note especially the flowering tree, the wall and crypt in the distance, which are the same tree, wall and crypt in all scenes (because, of course, all were shot on the same outdoor set at the show's Stewart St. studios).
It makes no sense for Giles to have book shelves in his school library that are not bolted down and can be toppled by a hard push. That would be a major health and safety code violation, especially since high school students have access there.