Lee says that the police arrested Ray "last night", but the arrest takes place in daytime and everything that is shown indicates that Ray was captured and escaped the same day.
The killer is wearing rubber boots, but when he runs his footsteps originally make the sound of hard-soled shoes on the pavement. His footsteps sound different a minute later when he runs through a water puddle.
Everyone says the killer is an "ax murderer", but multiple times it is shown that the killer use a meat cleaver, not an ax. The blade and heft of the two weapons are substantially different., and a simple forensic study would reveal that an ax wasn't used in the murders.
Ray tells Allison that he has to "go out onto the streets" to finish the investigation. However, nothing he does at the crusade brings him any closer to finding the killer. If he had gone out onto the streets in the first place to stop the killer, everything would have happened just the same. It's never explained why Ray goes undercover as a preacher when all he has to do is locate the killer on the streets and stop him.