Revealing mistake: At the end when Ted flushes the toilet and kills the priest, we see an outside view of the priest and if you look at the bottom of his robes you can see a black square thing hanging down from the inside which must have been squirting the water out of his robes. Also to prove this, you are not able to see any water coming from the drain in the ground, which does not make any sense.
Other mistake: The bishop that Dougal talks to about religion being pointless is supposed to be Irish but when he is telling Ted about his change of heart, the actor's English accent slips back in for a few seconds.
Chosen answer: It's characteristic of someone putting on a fake Irish accent.