At around 4 mins when Doyle looks at the board, under the red picture the lower right photograph depicts a woman, her arms hanging out to the right edge of the picture. Before and after the shot, this photograph is a row down.
When Agent Hull comes in Fenton's house, he sees the cork-board with Fenton's victim list. When it is first shown, the list is pinned up straight, with about a couple of inches of cork-board visible under it. However, when the list is seen again, it is slightly tilted, and pinned directly above a picture (with cork-board no longer visible).
[1:31:04]when viewing the FBI surveillance tape, the text reads PAL. PAL stands for Phase Alternating Line but it is not the video system used in North America. North American countries use NTSC.
When the boys are in bed at around 13 mins, Adam says "Goodnight, Curtis" to his pet millipede in a jar, not to his brother Fenton.
The flashbacks take place in summer, but were filmed in November; the actors' cold breath is visible, most notably when the trio bring Cynthia (first demon) into the shed and turn on the light.
The timing of light flooding the bedroom is a little bit off at around 17 mins when Dad opens the curtains in the boys' room because it was shot on a stage. In the director commentary, Bill Paxton adds "It doesn't bother me, stuff like that."
Choking kept in
At around the 15 minute mark as father and sons Fenton and Adam are sat round the dinner table eating the actor playing young Adam momentarily chokes on his food while drinking red liquid bill paxton gives a concerned look.
When Bill Paxton first encounters the angel in his bedroom, we can hear a broadcast of a baseball game. This flashback scene, as recounted by Matthew McConaughey, is supposed to take place in 1979. But the broadcaster refers to a player hitting .279 and stealing 73 bases for Lake Elsinore. There was no professional baseball in Lake Elsinore in 1979, and the only player to hit .279 and steal 73 bases for Lake Elsinore was Alfredo Amezaga in 2000 -- one year before the movie was released.
At approximately 19 minutes and 15 seconds into the movie, the teacher is writing on the chalkboard "The girl in the blue dress".
To the left of the teacher is a data outlet with an RJ45 type connector.
The RJ45 connector wasn't invented or standardized until 1987.
In the title credits montage, we see a newspaper which reads SECOND VICTIM FOUND IN GOD'S HAND CASE at 02:03. In the next scene, Agent Doyle tells his visitor that of the 6 victims in the God's Hand case, only the first body was ever found, while for "all the rest, only notes were found, no bodies."