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 (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.
And then you take the risk of the demon jumping out of his current host and into you. That's gotta hurt.
Of course, there are some precautions you can take that may not completely prevent you from being hurt, maimed, killed or scorned by society, but may lessen the risk: Be sure to bring holy water for protection (it also apparently causes burns on the host so obviously use it sparingly), a big cross (devils hate it and if it's big enough you can use it as a shield), earplugs (so you only hear things that are acceptable to human decibel tolerance), and board up the windows (devils have a habit of tossing priests).
And last—perhaps most importantly—try to perform the exorcism in a church rather than at a private home. Protection items you may need—crosses, holy water, pictures of Jesus, etc.—are close at hand.