I also don't get how super-speed would let you clean up a tape faster... none of the equipment has motors fast enough to catch up, and even if they did you'd just end up breaking the tape. (Assuming it's literally a tape. If it's digital, you hit up against the CPU, video processing is pretty heavy.)
I wish they'd just say "magic" and stop pretending there's any science involved in superheroics. "How did you clean up the tape in like 3 seconds?" "Magic." "Oh ok."