What's with that priest?

It's called Catholicism.

Just be glad Clooney didn't play a little boy.

Was the assassin's job really just to kill Clooney? So assassin goes to the target and asks him to make some weird specific modified weapon and mercury filled bullets it takes him weeks to do that then the assassin was about to kill him with a hand gun if not for some bus with kids. Then assassin is shooting, but somebody shoots her through the sniper scope she falls off the roof Clooney runs to her for several minutes and she is still alive to answer his dumb question. Then Clooney gets shot and drives to some river meeting with a prostitute( who must have had a GPS built into her head because I have no idea how she was supposed to and managed to find that same exact spot) instead of driving to the hospital. Are the directors and writers of this crap on serious drugs or do they think we buy this crap?

The priest was excellent. He knew The American was not truthful about just being a photographer, and I think he was genuinely trying to save him and offer him a way out of whatever life he is involved in. There's a deleted scene of Clooney in the church and the Priest tells him about some strangers in town, and how "I used to live in Napoli. And if you have lived in Napoli, you know the differenc between a fat wallet and a (in Italian) shoulder holster)". He's warning him that people are there looking for him. Clooney says "you're a good friend, Padre" and the the reply is "I'm a priest" as he walks away. I think he just wanted to try to stave off the bad end he saw coming for Clooney.