Deliberate mistake: There is one scene in the movie where Heath Ledger reads a Latin sentence in a book. As he is translating the sentence, he goes over the words one by one with his finger. This would never be possible in a Latin sentence, because words in Latin are never - I repeat: never - in exactly the same order as in English. Words that actually belong together can be placed on opposite ends of a sentence.
Continuity mistake: In the scene where Heath Ledger and his priest friend receive the dagger from the head of the Order that supposedly kills the Sin Eater, the head priest sets the dagger on the table between the 2 priests with the handle of the dagger facing Heath. The shot then moves from one side of the table to the other side showing different angles of the conversation, in each shot the dagger is no longer facing Heath but the other priest. But in the next shot is is, and so on for about 8 shots.
Continuity mistake: When Thomas follows the demon who is taunting him down in the sewers, there is a shot of him with a cut and blood on his face/nose. The camera changes to the demon and then back to Thomas, and the cut and blood are gone. Later, in the hospital, he has the cut back on his nose.
Plot hole: How did a woman who had just escaped from a mental institution get out of the country so fast? Even if she had a passport already, she wouldn't have it - the hospital or her family would. How could she get it back from them without SOMEONE turning her back in to the institution? It takes a lot to get involuntarily committed in the US, and I doubt she could get un-committed that fast, even with the guy she tried to kill vouching for her.