A Humvee is diesel, the sound it makes when it dies on the road is the sound a gasoline engine would make. A diesel would not make that sound.
When Lila picks up her mail, the flag is up on her mailbox. Having the flag up means the postal carrier hasn't picked up/delivered for the day.
The storefronts look nothing like Wabash Avenue, and there are no addresses on Wabash in the 20400 block. And Wabash is not on the south shore.
Jessica helps Luke pick out a tree at the tree farm, saying that it's the best tree because of its smell, among other things. In the next scene when they are driving, the entire top of the tree is white. It's clear that this is actually a fake tree, because if it were real, all that snow would've blown off as they drove.
The old car that Jessica's aunt agrees to drive has not been driven since her husband passed away, which was two years prior to this scene. However, they get in the car, it starts up right away and they drive off. If a car sits for two years without being started, the battery could be dead, or it would at least need a jump, especially in a place that has weather cold enough for snow.
In the exterior shot of the motor pool just before viewers are introduced to Carter and Angie, the flag on the building is a 48-star flag, last used as an official flag in 1959.