Plot hole: In 'Graduation Day pt 2' the Mayor has his vampires stand at the bottom of the steps leading out of the school to stop any escaping students. The thing is, all the parents managed to escape out the side exits. Since the Mayor was expecting all the students to try and run too, why didn't he have these exits covered? (00:33:15)
Continuity mistake: When Buffy wakes up in the hospital bed you can you can see the black strap of her tank top underneath the gown. Then when she gets out of bed on walk to Faith, and it shows her walking through the hall you can see a white spaghetti top through the gown.
Continuity mistake: When Wesley and Cordelia kiss, after a few seconds they freeze in place. Cordelia has her left arm around his waist, we see a shot of her face for about a second with her arm definitely angled downwards, then we cut to Wes' face and her hand's now on his neck. (00:25:20)
Other mistake: At the end the library that was rigged with explosives blows up. But the school's main entrance and the clock tower blow up as well, even though they are not rigged with explosives.
Answer: She has superpowers, ergo fast movement. The reason she outruns him so easily in "Touched" is that she stops trying to actually fight him and just dodges instead.
Shay