I just refinished oak floors in my new condo -- I did it before we moved in. After the sanding, there was dust -- a thin thin layer -- on every wall and surface up to about waist height.
So follow carefully the advice about either moving out during the project or really solidly taping up rooms to keep the dust from migrating from one place to the next.
Whether you can do spots or not depends on the current finish. What I've heard (and I did a moderate amount of research on this) is that it is very tricky if not impossible to "spot-fix" polyurethane -- it doesn't lap into itself. Meaning for a really seamless finish, you have to do the whole floor (perhaps stopping at a doorway or other natural border). Perhaps an expert refinisher would be able to minimize the visibility of a repair. Or a rug probably does a decent job :-)
I ended up using a product called Polyx-oil, made by a German company called Osmo. It's a finish that was relatively easy to apply myself and is very low toxicity. While there was an odor, it was really not very strong. There's a thread on uk.d-i-y called "Polyx oil - any experience of this?" with some advice, and I noted my experience. It is claimed, and having applied the stuff on my own floors, I believe it, that you can spot-re-finish this product. So if that's a consideration going forward...
I'll say one more thing before I finish: I don't recommend doing the sanding yourself. I did it once when I was much younger--and more foolish. It's a noisy, hard and dirty job. I am sure that there are improvements in the technology (this 4-disc sander mentioned by another poster sounds interesting), but . . . . Shop around, check Angie's List if it's available to you, get some quotes from pros, and think about what your time is worth to you. Especially if you are going to have to move furniture and do all this in time to save another day's rental of the machine...
Good luck! Jacque