Look for something with good zoom, but don't worry about the digital zoom. IMO, it is a gimmick. Picture quality really falls off when using it. Most HD cameras are between 20x and 30x zoom which is pretty darn good.
Also, look at purchasing a camera that either has internal memory, or uses memory cards for storage. Mini DV can be a pain to transfer to a computer and however long the video recorded is how long it takes to transfer due to having to record it to the computer.
One other thing to look for is image stabilization. It is hard to hold the smaller cameras steady, so image stabilization will keep you from getting sea sick watching your videos.
I bought a Sony HDR-CX130, after Jackalope said so many good things about it. I am really pleased with everything about it.
Great info cause I used it tonite for my boys soccer game and the square popped up and I wondered what the hell it was for.. I'll definitely remember it the next time.. How long are you getting out of a battery.