Just contributing to the answer already given, Ms. Swift was on VH1 this weekend saying it was one shot and describing the frantic nature of getting to your next position. She also said that this was take No. 18.
I’ve seen various one shot videos before and like the effect but I’ll agree that this one goes above and beyond the usual.
The Smashing Pumpkins Ava Adore is another one shot video. At the 2:35 the camera spins to reveal the dolly track and the crew. There seem to be a number of “cheats” as the band moves around pillars which may hide splices between different takes.
Apparently heavily based on Fischli and Weiss’ The Way Things Go, which must be the template for this sort of thing. As far as I can tell Fischli and Weiss did it for the lulz - there’s some guff about trying to capture the transient energy of their art installations, but I reckon they did it for the fun of it - and why not? The irony is that The Way Things Go clearly wasn’t one continuous take, although the process it depicts appears to have been a single event.
There’s a potentially fascinating but frustratingly imprecise database of average shot lengths for movies here, some of which have shots longer than entire pop videos. Béla Tarr features quite a lot. He never directed a pop video, as far as I know. Here’s a video of some people dressed in Mexican outfits serenading a floating thing. Manitoba? Manatee? Marmite?