Recorded videos can be viewed either by pressing the menu button with the camera active, or in the Videos menu, sorted by the date on which they were recorded. Connected to a computer you'll find them in a folder labelled DCIM on the device. It seems something of an oversight to me that there's no option to sync videos into iTunes.
It also seems curious that there's no option to reserve space on the nano's flash drive for video storage. As a workaround, you can use that setting as offered by iTunes' recently-added Autofill option, but it's an annoying omission. At least you can delete videos on the device itself if you're desperate to free-up some space while away from a computer.
The addition of a video camera brings with it two other new iPod nano features. The first is a fairly obvious one. Since there's now a microphone in the nano, Apple has added Voice Memos, which as the name suggests let you use the nano as a Dictaphone. The quality is as good as you could expect from a teeny, mono mic - a live gig recorder the nano is not.
Second and less obvious - in that it's completely hidden form view - is the placement of a speaker at the bottom of the nano. Given its small size it's inevitable that it sounds fairly tinny and weak, but that Apple has squeezed one in at all is frankly incredible and for showing off video clips to a few friends in a quiet-ish environment it's far, far better than nothing.
Also new to this generation is an FM radio receiver. About time too, considering just about every other MP3 player ever made since the turn of this century has had one. At least the implementation is well thought-out as it's possible to pause live radio broadcasts (for up to 15 minutes) and then listen to broadcasts delayed, or fast forward back to live transmission.
In a pretty gimmicky addition, the nano can now be set to use its accelerometer as a pedometer. The tracking is fairly accurate but it's no substitute for a Nike+ kit. I'd rather not waste the (minimal) battery life reduction on leaving this turned on all the time, though.