Everyone knows that tangling with the devil can, at the very least, result in burns, a broken neck, or impalement on a church spire. And then of course there are body fluids that may or may not end up all over you—huge amounts of spittle, vomit, tossed fecal material (yes, the devil is a bit of a monkey), etc.
And everyone knows that the possessed have brute strength and love to shake big pieces of furniture, so that's something to be wary of, too.
Then there's also the risk of a demon jumping out of his current host and into you. That's gotta hurt.
Of course, there are some precautions you can take: Be sure to bring holy water for protection (it also apparently causes burns on the host so use it sparingly, okay?), a big cross (demons hate it, and if it's big enough you can use it as a shield), and earplugs (so you only hear things that are acceptable to human decibel tolerance).
Last—perhaps most importantly—try to perform the exorcism in a church rather than at a private home where protection items you may need—crosses, holy water, pictures of Jesus, etc.—are close at hand.