Cordelia says she knows Giles was being questioned for a homicide case. However, during Giles' interview with the detective, the only time the word homicide was mentioned was before Cordelia entered the library.
Six minutes in, there is a chat in the school hallway during which Buffy takes three items out of her locker: a notebook, a thick textbook, and a book by Luigi Barzini Jr. titled "The Europeans." As she closes her locker, Barzini's book is right side up in her arms, but when next we see her a few seconds later, it is upside down, and the thick textbook underneath it appears to have been replaced by a much thinner one.
When Buffy visits Giles at his apartment, he is shown disheveled and and unshaven. It is later shown he fell asleep at his table when he answers Buffy's telephone call. However, by the time he goes to the library to see the gang waiting with Ethan, Giles is wearing the same clothes, but he is clean shaven.
Willow discovers the origin of the Mark of Eyghon, explaining that its "not Egyptian, it's Etruscan, mistaken for Egyptian by the design pattern, but any fool can see it pre-dates their iconography". However, the Etruscan civilization's earliest records are dated to about 700 B.C.E. while the Ancient Egyptian civilization came together around 3000 B.C.E. In other words, the Etruscans did not pre-date the Egyptians.
Buffy says she has to spend her allowance getting the tattoo removed, but it's much too early to be talking about it. Generally, one would have to wait six to eight weeks after getting the tattoo before professionals consider having it removed.
Ethan uses Sulfuric Acid to burn a tattoo off of his arm. The steam comes off of his arm before any liquid leaves the bottle, though.
When the zombie woman collapses next to Philip Henry on the ground, her arms and face have been made up to make her look appropriately dead, but her completely normal legs are visible below her skirt.
In the end credits, character names are garbled. Diedre spelled Dierdre, and morgue attendant, spelled mourge attendent.
When Buffy is being attacked by one of the fake doctor vampires on the hood of the car, you can see wires attached to the vampire's clothes just before Buffy kicks him away.
When Buffy breaks into Giles' apartment and kicks Jenny in the face, Jenny's stunt double is clearly visible while recoiling from the kick.
Eighteen minutes in, in the computer lab, Cordelia informs Buffy that the police were talking to Giles in the library about a homicide, but there is no way she can know this, as Giles was informed before she arrived in the library and no mention was made of why the police were there while Cordelia was present.