At the old gym everyone was getting staph infections because the Krav Maga guy wore their shoes on the mats.
At my new gym we use a weed sprayer to cover the mats with disinfectant everyday, letting it dry overnight. No one is allowed in the training area with shoes on.
I wash the scratches and mat burn before I leave the gym. Sometimes wipe it down with an alcohol pad.
When I get home I always jump right into the shower and wash up with a Japanese scrub towel. It's a towel that has a sandpaper like texture. It seems pretty good at removing the nasties from my skin.
It looks like this.
http://www.crossfit.com/discus/messages/21357/33425.jpg