When Angel and Buffy are fighting in the woods, he is barefoot. Later, when she visits him in the mausoleum he is wearing shoes.
Oz's werewolf form in Beauty and the Beasts (1998) looks completely different from his werewolf form in Phases (1998).
Buffy has a two o'clock appointment with the school counselor, but the wall-clock over the door shows a quarter past four.
When Debbie turns around from looking in the mirror, her black eye is gone.
During the wrap up, Xander mistakenly calls Cordellia "Cor" which is Faith's nickname for her. However, the way Xander has been fangirling over Faith ever since she arrived, it is plausible for him to semi-consciously adopt it.
Willow, Xander, and Cordelia go to the morgue to examine a corpse. While they're examining, you can see the corpse breathing.
Angel came back from Hell more or less a feral creature, so where did he get his pants from, and how did he remember that he needs to wear pants?
Giles berates Xander for falling asleep on Oz watch. But when Buffy takes a turn, Giles comes in to find her asleep and says nothing.
There is great confusion the day after the first murder as to whether Werewolf-Oz escaped from his cell the previous night or not. Since there is no doubt that Oz was in his cell in the morning after, what Giles actually implies is Oz might have woken up outside after the murder, crawled back in through the window to throw the Scoobies off, and is lying about it. Which then does not match the rest of their discussions.
Another book shelf in the library is pulled down on another pupil. One should think at the latest, this code violation would have been finally fixed and the shelves bolted to the walls or floors after Willow was hurt that way in Becoming: Part 1 (1998).