HI Anne,
I agree with Nathan, it's unusual to see feet shredded, I certainly haven't in the 13 or so years I've been doing this. Get a few mat burns and such, but like Nathan says, these callous over after a while.
In most dojo's you'll find shoes to be a definate "no no", although there may be one or two out there that like to train with them. For the most part this is to protect the mats and preserve their longevity since they cost the earth to replace.
Aside from normal socks, which don't work for me, Japanese tabi are the best thing you can use, there are a couple of links to suppliers in this thread
http://www.aikiweb.com/forums/showth...highlight=tabi
Use the tabi whilst your feet heal, then go back to bare feet again.
kind regards
Bryan