I found thisforum great for research and want to pass on my experience. I ended up buying the Nikon CoolPix 3700, $130 after $100 rebate (expires this month). It is TINY, but easy to hold with nothing in the way. It records about 5min of 640X480 at 30fps on my 512mb SD card. You can plug it directly into a TV for movie and slideshow playback (cableincluded) which is very cool. Picture quality is great for 3MP, and the flash is as good as any on a subcompact camera. It is also very fast to boot-up and focus. If your requirements are a compact camera for family snapshots plus TV quality video, I cannot think of a better camera.
For general family videos (i.e. short snippets) I don't know why anybody would get a mini-DV (tape) video recorder. This camera does it all. Besides recording length, the biggest limitation ofapoint-and-shoot camera over a dedicated video camerais the viewfinder does not rotate upwards... but this is a reasonable trade-off.
Happy filming! -Henry