Yeah, the paper does eventually get dirty if people are standing on it. You've just got to do the best you can to try to make sure their shoes are relatively clean, and have a towel laid out on the floor by the paper that they can wipe any loose dust or whatever off their feet before they go on.
Even though you may need to stretch out about 15ft of it to be able to get your shots, when you come to tearing it off, you'll probably only be tearing off a couple of feet at a time to get fresh.
What a few I know do, is pull out the white seamless, then lay white vinyl or a reflective white hardboard on top of it for the subject to stand on (so you get the nice reflection). The vinyl will simlpy reflect the whiteness on the background and be blown out, so you won't see the join behind your subject.