When John consults the supernatural expert/book author Albert Leek in the library, Leek refers to other times Mothmen have been sited before big disasters. He mentions the Galveston Texas hurricane of "1969" yet alludes to the big one that happened in 1900 and killed about 6000 people.
When Mary is examined for the brain tumor, we see how her head is placed into the head coil of a MR (Magnetic Resonance) scanner. However, when we see her being placed into the scanner itself, she is being placed into a CT (Computed Tomography) scanner. Those type of scanners does not use coils.
After John's car stalls, he gets out of his car and looks down at his shoes. He is wearing dark brown or black, glossy dress shoes. A few minutes later, when he is standing in Gordon's shower stall, John is wearing light-brown, nu buck casual shoes.
John passes a sign for Maine Avenue as he leaves Washington, driving from Memorial Bridge to Interstate 95. Maine Ave is in the opposite direction and there are no signs for Maine Avenue on any of the roads he could have taken to get to I95.
On Klein's drive from Point Pleasant to Chicago, a glimpse of an exit sign for "New Kensington" can be seen. There is no "New Kensington" between West Virginia and Illinois, but there is one near Pittsburgh, where the movie was filmed.
In the scene where John Klein is talking on the phone explaining that he didn't leave the voice mail about the chemical plant, he walks to the mirror and the mirror doesn't match what he was doing. His body movements were a few seconds ahead of the image in the mirror. (This may have been intentional due to the paranormal nature of the film, but they may also have had to add in the mirror image later because the camera was visible and not synchronized it properly.)