Nah, as long as they can be pieced back together, the cash is still good.
If a business won't accept them all taped up, the U.S. Treasury will happily replace them with brand new bills.
I'm trying to devise a catchy line to say about this video, but my mind is, cough cough, going blank for some reason.
http://www.youtube.com/watch?v=8QG7p8jH4jI