(Around 35 minutes) Ryan puts his hand out to fist bump James Blake but in the close-up his thumb his extended.
The silver metal trash dumpsters, seen when the TARDIS lands at the beginning and when Ryan and Yaz hide from the officer, are European and modern.
In the opening scene set in Montgomery, Alabama in 1943, we hear the song "Woke Up This Morning (With My Mind Stayed On Freedom)". The song in that form was not created until the early 1960's.
In 1955, leather jackets (especially over white t-shirts) were associated with New York City criminal teenage gangs, and the only young men who wore beards were beatniks. Both would have drawn considerable negative attention in the American South, probably including from the police. Yet Krasko moves and interacts freely around Birmingham without prompting any comment.
American bus driver Blake refers to a change in the company's "rota", a word that is chiefly British for a personnel schedule.