There are the more obvious obstacles: your friends, family, and co-workers don't follow the same schedule. It's lonely for anyone who values social connection. Unless you work on your own, the workplace is a bad environment for sleep.
There are also potential health concerns for certain polyphasic sleep schedules. Most polyphasic sleepers don't sleep a full ~8.5 hours in a day. Your body uses sleep to refresh your body and keep the body (particularly the circulatory system) running strong. On my schedule, I started by sleeping about 5 hours. I was monitoring my blood pressure, and while it remained within a healthy range (I was in my mid twenties) the variance was much greater than it was on 8.5 hours. When I went to sleep late at night, my BP was quite low.
The long-term health effects aren't well known - there aren't many people to study, and a clinical trial would be all but impossible (people would likely not adhere to it). We can make some guesses, though. For one thing, you're altering the way melatonin and cortisol work in your system. Messing with your body's chemical and hormonal balance usually doesn't turn out well for health.
We have one group to compare with: people who work night shifts. Studies have shown they're at increased risks for heart problems, ulcers, obesity, depression, some cancer, other gastrointestinal diseases, and possibly more. (Just Google it or use Scholar: http://scholar.google.com/scholar?hl=en&q=night+shift+worker...) I certainly experienced depression.
There are other things that are just annoying. As someone else stated, coffee is a bad idea, and so is alcohol, and I enjoy both. Most people will have to decide between holding to a schedule or attending others' events. You'll probably either eat worse at night or have to cook more. Nothing is open when you're awake. The list goes on.
I don't recommend it, but if you DO think you want to try it, still, here are some suggestions:
-You must have a completely dark room to sleep in during the daytime.
-Avoid coffee and alcohol. In fact, cut coffee and alcohol out before you change your sleep schedule. Doing both (especially if you rely on coffee) will be quite a shock.
-To adhere to the schedule, you'll have to think of what you're going to do when no one you know is awake. You need to schedule things.
-Don't forget to schedule social things. I tried to be wake up before 7 PM when many social things seem to start.