The patches on the sheriff and the deputy's shirt and jacket, as well as the decal on their SUV, read 'Bleuclair Parish' which is incorrect. Shreveport, Louisiana would be in Caddo Parish.
The brothers are shown using a hatchet and an ax to cut wood for Charlie's funeral pyre. But the ends of all the logs we can see are clean cut by a chainsaw.
When Dean throws Cass to the floor, you can clearly see that it is not Jensen Ackles, but his stunt double.