It seems that if you use the remote's power button the lights at the bottom turn off. If you use the Wii's power button they don't seem to. While this might not effect anything, if it makes you feel better at night.
Just remember, there is a lot of stuff going on in that remote. It's running bluetooth, it's managing 3 motion detection systems, computing basic triangulation, powering a speaker, and vibration.
The batteries it came with lasted about 27 hours of use (mostly Zelda). That's around the numbers I've been getting from others. If you're in that ballpark I'd say its just time to buy rechargeables. Sure it says not to, but does my digital camera and I've noticed no ill effects.