It's called multitrack audio recording, and commonly runs on your run of the mill laptop. HD video would probably be a few orders of magnitude more data than that, with even more processing.
Computers are really, really good at these kinds of things if only the software is efficient enough.
Your run of the mill laptop is a wonderful machine capable of amazing things. But that laptop is not rated to withstand extreme vibration and shock and huge temperature ranges. Nor does it have the external interfaces to deal with large numbers of custom, high speed digital data buses, nor does it contain the signal conditioning hardware to deal with a huge array of transducers working with differing physical phenomena, each with its own unique power and signal processing requirements. The system I support has to deal with all of these things, plus more constraints than are relevant to the conversation here.
Much (but not all!) of this doesn't even require a general purpose computer. It can be done with state machines implemented in FPGAs.
Sometimes you need something different than a run of the mill laptop.
Like I said, you do have a very good point. I am often frustrated by the realization that my laptop is much more powerful than this specialized data collection equipment. But we have a very large fixed base of equipment, with no plans to upgrade anytime soon.
EDIT: I would like to know how other flight test people visualize their test data. Seems like you can only make so many envelope charts and strip charts (they work and are effective, but man, sometimes I'd like something different)
So: some quick googling suggests that "economical cruising speed" of an Airbus A320 is 840km/h [1]. After quick back-of-envelope calculations, this gives ~230m/s, so 0.2m per 0.001s. Given some possible uncertainty of a single measurement, I'd imagine that's not unreasonable level of precision when e.g. your Airbus is landing on an airport.
[1]: http://www.airliners.net/aircraft-data/stats.main?id=23