While from the inside of the car, the window is rolled down, from the outside it is clearly not.
Loy and Ebal are sitting in the diner. Loy gets the sugar jar, pours sugar in his coffee and leaves the jar on the table. Then the camera changes to Ebal and Loy has the spoon in the coffee with his hand holding the spoon after he finished stirring the coffee. After that, the shot comes back to Loy and he is holding the jar ready to pour sugar again and the spoon it's not now in the mug but he is holding it horizontally on top of the mug.
Leon mentions to Loy "this new cat" named Dizzy Gillespie. In fact, Gillespie had already been a major jazz star for several years, having risen to fame during the war.
As the cars drive through the neighborhood, it is clear that the sidewalks at the street corners have been adapted for handicapped use, which would not have been the case 70 years ago.
Timothy Olyphant says he is a priest of the Mormon Church and a member of the Quorum of Seventy. "Priest" is part of the Aaronic priesthood, where a member of the 70 holds the Melchizedek priesthood, you wouldn't be both. Its like saying he is a Sergeant and a Colonel in the US Army.
In the diner, Doctor Senator says, "after the ceasefire", but WWII ended in a surrender; WWI ended in a ceasefire on 11 November 1918, before being resolved by the Treaty of Versailles in 1919.