Close-ups of the Chevy truck's headlights alternately show round and rectangular lights.
Luke uses the mains voltage AC generator to jump start the 12v DC Chevy. The most likely results would be a "fried" battery, blown lights, possibly blown alternator diodes but definitely no jump start.
In multiple scenes, the chemical lights aren't apparently lit despite having been just recently activated. They should remain lit for several hours; however, it is made clear from quite early on in the movie that energy, whether it be in the form of electricity or combustion, isn't behaving in expected ways. It is therefore reasonable to assume that chemical lights would be affected as well.
When Luke is in the 7 Action News building, it is clearly daylight. The next scene says "72 hours later" and it's dark outside. 72 hours = exactly 3 days later, thus it seems it should be daylight again. However, it is later explained that hours of daylight became shortened as the phenomenon depicted in the film lingered.
The jukebox plays CDs but suffers from vinyl-style slowing down of the music when the power drops.
While Paul is dreaming, he walks down a long corridor in the basement. He opens a door at the end of the corridor, only to discover a brick wall. When he starts banging on the wall with his hands, the wall shakes as if made from cardboard.
A gasoline powered generator is in continuous use in the bar's basement throughout most of the movie, giving off clearly visible fumes. No one is even bothered by this, let alone asphyxiated.
A full size pickup truck crashed into the doors of a church. When the wreckage of the truck is revealed from the outside there is no damage to the six steps that the truck must have slammed into in order to have crashed into the church doors.
Paul explains that the darkness had taken him when his visual light went out, and then found himself reappeared back to life again with a head injury after his visual light reactivated on again. That goes against the whole plot of the movie, and the characteristics of the darkness of once it takes you you're gone, there is no coming back.