The light was always outside the confessional box and would be switched off either if someone was occupying the confessional by the priest or if no priest was available. This is not a goof.
When the girl struggles with the demon in the hospital, a sonogram of the fetus is shown several times, but there is no ultrasonograph present in the room.
After the exorcism scene, from the moment Colin O'Donoghue plays with the nail, he looses his American accent and Irish accent takes over for the whole scene when he talks with Anthony Hopkins.
The Kovak & Son Funeral Home is supposed to be set in Dixon, Illinois, as seen in the letter from Italy that Michael Kovak (Colin O'Donaghue) gets at the end of the movie; however, the area code for the phone number on the funeral home sign is "312," which is an area code for Chicago (over one hundred miles away from Dixon).