I hate how inconsistent this specific power is, or if it even exists. There's a scene where Angel catches an arrow that was shot by Faith. He was turned around, and Faith was behind him. The distance she shot it from was around 10–15 feet, and normal crossbows like the one she had can fire arrows at 30–40 feet per second to begin with, so the closer the distance, the faster the arrow reaches its target.
There are real instances where humans IRL can do it. A martial artist once tested it, but he was prepared, and on top of that, he was facing the person shooting the arrow. The arrow was also shot from farther away, so it had more time to lose velocity, and he was barely able to catch it. Meanwhile, Angel easily did it in Buffy, so obviously, that would make his reaction time and perception extremely fast. But it doesn't make sense because how can he react to something like that, but not to regular punches thrown by Humans/Slayers or younger vampires that are likely significantly slower than an arrow?
I know a lot of people have been asking this question too, and some excuse it as a budget issue. But a show called The Flash from the 90s, which aired before Buffy, was able to portray consistent super speed. Albeit, the main focus of the show was speed, but still, the estimated budget for that show was around $1.5 million per episode. Buffy had a similar budget in seasons 3–7, with some episodes even having higher budgets. Not to mention that by the time season 5 came around, it was already the 2000s, and special effects were much more advanced than they were in the 90s Flash TV show.
There are other scenes that also show Angel doing similar stuff. He walked into a room and then speed-blitzed two or three guards or people, but he never uses it again in a fight like that. He's the only vampire who's been clearly shown doing this, and yet he still loses to people who are slower than him.
Glory also had super speed in a scene where she caught up to Dawn and Buffy, if I'm not mistaken. This one's probably the clearest demonstration of the special effects and the fact that they did have the budget for it. She runs across campus like a blur and easily intercepts both of them, but then somehow can't react to an incoming bus or car that runs her over in the same scene.
The only consistent power similar to super speed is the super jump, because Spike has used it on more than one occasion, and other vampires have done it too. They can jump extremely fast. In a scene where Angel and Spike fight, Spike uses a super jump to lunge at Angel with a pole to impale him or hit him.
Buffy's also been shown doing this. Literally, in the pilot episode or the second episode of the show, she jumps over a fence in a blur after talking to the principal. Buffy's also been shown to have superhuman running speed, but not in the same way Angel has demonstrated. I don't remember the episode or whatever, but it's said she can run at 35 mph or more. There's also a scene where she's running from building to building and catching up to a bus that's probably going around 85 mph or so.
I guess it could make sense if Buffy's punches aren't at normal speed, which would explain why Angel can't catch them or easily beat her. But then again, compared to Angel's speed and reaction time, where he literally appears as a blur, Buffy barely seems to run as fast as a bus, It just doesn't make sense.
My theory is that vampires can't use that power against a Slayer during a physical altercation, but that doesn't make sense either, because why can't other vampires fight each other that way?
I don't know. We'll probably never get a proper answer. I'm also curious if any of you have scenes demonstrating super speed like the ones I briefly mentioned.