When Katherine is giving Ben her list of causes for the 10 plagues, she states that locusts would have been blown into Cairo. The plagues took place around 1400BC, but Cairo didn't exist until 969AD, and didn't become the capital until 1168-1169AD. She should have used Thebes as the reference city since it did exist then, and was Egypt's capital.
When Kathrine walks up in the girl's house for the first time she has a smaller circular barrette in the back of her hair. A short time later the barrette suddenly changes to a much larger rectangular one.
When Katherine and Ben are wading through the river of blood, Ben stumbles and the left sleeve of his shirt and his bag dip into the river and become visibly wet. A short time later, when frogs start raining from the sky, both his shirt and the bag are completely dry. Even if there were time for the shirt to dry, the blood in the river would inevitably leave a stain.
When Katherine talks to the boy at the cattle farm, he is drawing with crayons. In the "over his shoulder" shots he is using a green crayon. In the "across the table from him" shots, he is using a blue crayon.
The young boy colors in some yellow in the lower left corner of his drawing showing the young girl and the dead cattle (adding to a little yellow already present). But when the female miracle debunker pulls out the drawing later, it had only the tiniest hint of yellow.
The city shown as "Concepción, Chile," at the beginning of the movie is nothing like the real location. Concepción is located along a river (the Bíobío), not a sea, and has a cold and rainy climate, many modern buildings (especially in the city center, where the cathedral is located), and no heavy industry. Additionally, the Chilean police uniform is dark green, with long jackets and boots and no beret, and Chilean police and Armed Forces personnel are not allowed to wear beards, only mustaches with superior officer approval.
In the slide show presentation in the beginning of the film, there is a slide show displaying both methanol and ethanol. However, the molecular structure labeled as ethanol is in fact methanol, and methanol is labeled as ethanol. Also, the structures displayed for both other chemicals on the same slide, DMSO and benzene, are incorrect.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
When they visit the brother in the morgue, his body is deeply decomposed and they are surprised, saying that when he was brought there three days previous his body was pristine. Later in the movie they show the scene where the brother dies, and his body is immediately decomposed, so there was never a time where his dead body would be pristine. However, as revealed later in the film, the entire town is involved in the same cult and could be lying to Katherine to keep her from figuring out the truth.
If Loren is in fact an angel, sent down to earth by God to counter Satan's sect in the town of Haven, and Katherine was sent for by the same sect to kill her, it seems illogical that God would burn her pictures in a Reaping-symbol as some sort of warning. Unless it was meant to warn her not to kill Loren, in which case it is strange that God would have Father Michael Costigan die in a fire as he was talking to her. Unless these events are triggered by Satan, whose presence and powers are completely absent from the rest of the film.