The wireless Guitar Hero 3 controller has a small design flaw which can make it a pain to play. The detachable neck is connected by plates which are supposed to press against each other; however, if it is loose in the slightest you'll have problems with the fret buttons registering, as Detty said. I used
this idea to fix mine, and it's worked perfectly thus far. It pisses me off that I had to do it in the first place, but it does work well.
When it's working fine, it's my favorite guitar controller I've used thus far. Fret buttons are easier to press, whammy is loose but still really springy, and it seems to have better response than some of the other's I've used. When it works the way it's supposed to I love it.
Battery life really isn't that bad; I can play for a little under a week on a standard pair of AA's. There is a rechargeable battery pack
available from Red Octane, but don't really know much about it asides from the fact that it exists.