When Dagny gets in her car after leaving the roadside diner in Brandon, WY, the license plate is a red Colorado plate. When she arrives in Wyatt Junction, CO, the plate is a county 22 Wyoming plate. Same car, different plates.
In the opening minute of the movie describing the economic turmoil taking place in 2016, there is a quick image of an article from Trinzinca dated "Sunday, 18 June 2016". However, June 18, 2016 will be a Saturday, not Sunday.
The change of seasons in the Colorado scenes clearly do not match the dates shown in the film. The aspen trees are always shown at the beginning of their seasonal change, which would take place in late September and into October and would not be seen at other times.
About 10 minutes into the film planes can be seen flying over the train. Trains, and not planes are the affordable form of transportation, as planes require oil based fuel, a commodity too expensive for the times.