Deliberate mistake: Every time the commandos are seen in the early episodes of this season (The Freshman and Fear, Itself) they wear ski masks to protect their identities. Starting in The Initiative, they stop doing this. The reason is that the audience needs to be able to identify the different commando characters, but it's still a discontinuity.
The Freshman - S4-E1
Visible crew/equipment: When Buffy and Xander are doing some research, check the left side of the screen in a wide shot, when Xander asks "how far back do the disappearances go?" You may need to turn the brightness up, but there's a boom mike bobbing around. (00:34:25)
The Freshman - S4-E1
Continuity mistake: When Buffy is fighting the vampires at the end of the episode, she grabs a tennis racket and smashes the brunette vampire over the head. She falls over the back of the couch and we hear the thud of her landing, however in the wide shot of the couch the vampire has just started to go over the back.
The Freshman - S4-E1
Continuity mistake: When Buffy is talking to Giles after his run, his towel moves from being on one shoulder to being across his back and over the other shoulder to being back on one shoulder.
Continuity mistake: In the scene where Buffy and Kathy are deliberately infuriating each other (tapping pencils and cracking eggs) there are several lights on throughout the room (on Buffy's desk, above Kathy's computer, in the kitchenette) yet when Buffy turns out her bedside lamp, the entire area is thrown into darkness.
Continuity mistake: When the portal is opened Buffy crawls around to the other side of her bed yet just as the portal closes there is a wide shot and she isn't next to the bed.
The Harsh Light Of Day - S4-E3
Continuity mistake: When Spike pins Harmony to the wall, his hands change from flat against her to grasping her shoulders, depending on the angle. (00:12:00)
The Harsh Light Of Day - S4-E3
Continuity mistake: When Buffy catches Parker talking to another girl he stands up to leave and slings his backpack over one shoulder. In the next shot it's over both shoulders. (00:34:45)
The Harsh Light Of Day - S4-E3
Continuity mistake: When Spike finally gets into the area where the gem is and Harmony follows him up there, he puts on that necklace thinking it's the gem. When he realizes Harmony has the gem it shows him taking off the necklace. It cuts to another shot and then shows him again with the necklace, but minus the charm.
The Harsh Light Of Day - S4-E3
Other mistake: We've seen before that vampires are fine as long as they aren't in direct sunlight, yet in this episode Spike is in the shade when Buffy removes the ring and he still starts fizzling.
The Harsh Light Of Day - S4-E3
Continuity mistake: When Spike and Harmony find the treasure room containing the Jewel or Ring of Amarah, after Spike stakes Harmony he removes the necklace he had on, but in the next shot he's wearing the necklace again.
The Harsh Light Of Day - S4-E3
Revealing mistake: When Buffy is fighting Spike, she throws him against a table and then runs over it; you can see this is her body double. It is extremely obvious.
The Harsh Light Of Day - S4-E3
Continuity mistake: When Spike is in the area where the gem is located, he walks to the right of entry hole, where he finds the gem. Then Harmony appears from the right side of the screen, where there's obviously no entrance.
The Harsh Light Of Day - S4-E3
Continuity mistake: When Buffy and Spike are fighting on campus during the day, Xander tries to help Buffy but Spike throws him against a lamppost. When he lands in the ground he falls completely on the grass on his side but if you look behind Spike in the next shot he lies half on and half on the grass on his front.
The Harsh Light Of Day - S4-E3
Continuity mistake: Right before Spike jabs Buffy in the face on the college's campus, there are a ton of people around. But after he jabs her in the face and they start fighting, all of the people are gone.
Continuity mistake: When Xander is showing Willow and Buffy his fake ID and the view of the shot is from behind Xander, he is holding the card with his thumb and middle finger. Switch to the view from behind Willow and it's being held with his thumb and index finger. Then it switches to behind Xander again and it's back to thumb and middle finger.
Continuity mistake: When Veruca comes to Oz's cage to spend the night there, she tosses her jacket onto the round stone thingie (knob?) at the end of the stairs, and it covers the whole thing. However, when Willow discovers them in the morning and Veruca goes to pick up her jacket, you can see that it has moved. Willow didn't touch it when she entered, and both Oz and Veruca were locked up so they couldn't get anywhere near it. (00:26:35 - 00:29:20)
Visible crew/equipment: At the very end of the scene where Buffy and Giles discuss what happened (including The Initiative), you can see the microphone at the top of the screen. (00:39:45)
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