In the cemetery, right after Angelus has risen, both Angelus' and Darla's breaths can be seen, suggesting that their breath is warmer than the air. Vampire breath should be the same temperature as the air.
Placement of Cordelia's hands holding the security folder.
Wesley claims to be doing a vivisection on the remains of a demon. However, a vivisection is only done on living specimens. What Wesley has done would be more aptly described as an autopsy, or a post mortem.
The groundskeeper seen in the graveyard, in 1753, is holding a lantern that is clearly battery-powered.
On Buffy's 17th birthday (January 18, 1998), Angel stated he was 241 years old. This episode posits that he was turned in 1753; that would mean that, even if he wasn't counting his time as a human, he would be at least 244 in 1998.
When Angelus has just emerged from his grave, Darla encourages him to feed from the Grounds Keeper. Angelus goes into game-face with fangs and attacks the Grounds Keeper's neck. We can hear him drinking, actually slurping; but immediately afterward, there is no blood on his mouth or teeth.
In the scene where Angel visits Kate Lockley in her office at the police department, the boom mic is visible when Kate is going through her filing cabinet.