Visible crew/equipment: When Buffy meets Giles in the library after the opening credits, and they start talking, throughout the scene, you can see set lights and reflectors reflected in Giles' glasses multiple times. This happens often throughout the series, but is particularly noticeable here.
Out Of Mind, Out Of Sight - S1-E11
Visible crew/equipment: After Cordelia wins May Queen, Buffy, Xander and Willow are talking, and right before she walks away, you can blatantly see an on-set light reflector being reflected in Buffy's sunglasses.
Out Of Mind, Out Of Sight - S1-E11
Visible crew/equipment: When Giles, Willow and Xander are trapped in the storage room with the leaking gas, at one point you can blatantly see a massive set-light reflected in Giles glasses. (This is fairly common, as often lights are reflected in his glasses, but it's particularly noticeable here).
Out Of Mind, Out Of Sight - S1-E11
Visible crew/equipment: When Angel and Giles talk in the library, in multiple shots you can see stage lights and light reflectors being reflected in Giles' glasses. (This is actually fairly common in many of his scenes, but it's particularly noticeable here).
Never Kill A Boy On The First Date - S1-E5
Visible crew/equipment: When Buffy and Giles are in the cemetery, right before Buffy bails to go meet Owen, you can blatantly see a number rectangular studio/set lights reflected in Giles' glasses coming from various angles. (There wouldn't be dramatically-angled lights like that in a cemetery, let alone after dark).
Welcome To The Hellmouth (1) - S1-E1
Visible crew/equipment: When Buffy's mom drops her off at school at the beginning, watch closely when Buffy gets out of the car. In the passenger door's quarter glass window, you can see a reflection of a set-light (probably a fill light to eliminate shadows) for a few seconds when she opens the door.
Welcome To The Hellmouth (1) - S1-E1
Visible crew/equipment: In the beginning, when Buffy is having the prophetic dream, there's a shot right as it's about to end where the camera is above her and moving down closer to her. If you watch, you can blatantly see a shadow (more than likely the camera rig) grow over her as it gets closer and closer to her.
Visible crew/equipment: When the 4 Scoobs meet in the hallway for the revolving shot, just as the camera starts to pan over you can see someone casually walk down the hall into frame behind Xander's left shoulder, as the camera starts to revolve you can the person is now crouching in the shadow behind Giles. It appears to be a crew member that accidentally walked into shot at the wrong moment and hid quickly.
Out Of Mind, Out Of Sight - S1-E11
Visible crew/equipment: When Buffy and Cordelia enter the mop closet you can see the shadow of the boom microphone on the wall near Buffy's head (left side of screen). (00:31:44)
Visible crew/equipment: When Buffy is going through the murdered Professor's office, Angel seems to trip through the doorway. To the top right above Angel's head a boom mike is visible twice.
Visible crew/equipment: When Buffy and Riley are talking at the crime scene, where he tells her about Maggie Walsh's death, one of the camera shots has a very visible black border around the entire edge of the screen as if the lens shade was visible in front of the lens and could be seen in the shot. (00:18:20 - 00:19:40)
Visible crew/equipment: After Buffy walks outside to hear the sirens, in the close up of Buffy's face on the upper right corner of the screen you can see a boom mike. (00:06:30)
Visible crew/equipment: In the final scene where Buffy apologizes to Dawn, a microphone is visible in the upper left corner, from the camera angle behind Dawn, just after she says "you hurt my arm." (00:40:00)
Visible crew/equipment: When Riley goes to Spike's crypt to ask him for information about Dracula, the microphone appears in the upper right hand corner of the screen. (00:17:55)
Visible crew/equipment: In the scene where Spike escapes from The Initiative a black curtain can be seen to the right of the screen after the other vampire is release from his cell. The curtain serves no purpose to the set or scene and it disappears in the next shot. (00:13:25)
Homecoming - S3-E5
Visible crew/equipment: When Buffy and Faith are in the library, a person's arm wearing a white shirt can be seen on the left side of the screen behind Buffy in one shot.
Visible crew/equipment: When Giles picks Buffy up in his car, you can see lighting and camera equipment on the right.
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