When everyone is escaping the fairgrounds after Dale steals the governor and they end up getting in the car, and when Russel clears the way through the building you can clearly see the roof fell in Jakes path, but on the next shot the roof is missing completely.
When Jake and Russel are looking at the map of destroyed cities, in some angles, it's snowing, while in others it's not and there is a clear blue sky overhead.
When Johnston Green tells Jake that he is 59 years old and was the mayor (earlier stated 25 years in the position) and then a retired Ranger with combat time (20 years in military to retire) he would have had been 14 when he entered the military.
When getting in the car fleeing the market, the camera and crew can be clearly seen behind Heather.