See Kids with Cameras, which we should emulate everywhere. There are a number of other such organizations.
The primary limitation of the OLPC for video editing is local storage. Assuming that there's 1G of storage, that 200MB is occupied by system code, and that half of the rest is used for other documents: that leaves 400MB, or, at a decent level of compression, about 15-25 minutes of video. If you're actually editing the video, at least half of it ends up unused, so really you have enough material for little more than a 5 minute short.
If you can rely on the backup storage, however, you could easily expect 3-5GB to be available to those editing video. This becomes more realistic/useful.
The trouble, then, is the network: using maximum throughput, without saturating and killing performance for the rest of the mesh.
Is there a way to get off the mesh and request a direct connection? The servers should have enough antennas to accomodate this, so it's more a matter of software.