During the woman's speech at the beginning, a car alarm goes off, but when it cuts back to Willow speaking, there's no alarm.
When Xander falls into the hole while digging, there is one brief shot when he is lying on the ground and his shirt has gone from gray to black (probably the stunt double).
Due to standards concerning cultural resource management, a site survey would have been performed by archaeologists prior to ground-breaking, making it unlikely that the mission would have gone unnoticed before Xander started digging, considering it is only a few inches beneath.
When Anya says, "Xander said he was gonna dig", Buffy's shoulders twitch, apparently with Sarah Michelle Gellar's laughter. At the next line, Buffy twitches again and starts to turn to Willow. In the next shot, she is already facing Anya again.
During the attack on Giles' house, Spike is hit with several arrows. At one point, when he is talking to one of the attackers, the two sides of the arrow piercing his shoulder wobble as he moves.
(at around 37 mins) When one of the Native American guys jumps through the window, on the left you can clearly see hands, presumably to keep the decor up while the actor jumps through the glass.
At 38:55, when the view cuts to the interior of Giles' apartment, part of a lighting instrument is visible at the top edge of the picture, along with a bit of power cord.
When Willow, Xander, and Anya run into Angel, Anya asks if it is Angel and that it's the first time they met. In fact, Anya had met Angel back in Doppelgangland (1999) at the Bronze even though they had no dialogue between them.
Spike is hungry and complains, 'an entire siege, you'd think one of you would bleed a little.' Buffy was cut and bled twice during the battle. Even if Spike didn't see these incidents, he would have smelled her blood.