The only reason I loved this episode was because it was heavily focused on Prentiss who is one of my favorite characters, and it was exciting to get some character development. I, however, was a bit unimpressed with the un-creepiness of the exorcisms despite the majority of the reactions I've read on here, and the ambiguity of the actual plot. It didn't seem very well thought out to me. That being said, I thought it offered a few interesting perspectives on religion, which I love seeing every now and then because I love controversy.
As for the nose bleed at the end, I've noticed a lot of people questioning to its cause.
We may recall Emily questioning the priest, accusing him of splashing his victims with holy water that contained some kind of chemical (though I don't recall what it was called) which was causing the bodies of his victims to give out.
We may also recall the moment when Emily and Derek rush into John Cooley's house to rescue him. Prentiss shields John as Morgan detains the priest, but not before he splashes a final amount of holy water on both Cooley and Prentiss (note her line: "What is in that water?!").
I'm assuming the nosebleed is a small residual symptom of the chemical she was exposed to, though obviously not enough to do much damage, but ultimately proving that she was right the whole time.