On election day the leaves are still on the trees and green. In New Jersey they would have turned colors and be falling off.
The ship Alvin boards with other British troops before his mission is clearly a Liberty Class cargo ship. Although British in design, Liberty Ships were commissioned by Franklin D. Roosevelt in 1941 to assist Britain's war effort. As in the alternate reality of the series Roosevelt is not president and the United States is isolationist, Liberty Ships should not exist. Moreover, Britain did not employ especial purpose vessels as troops transports, as they used ocean liners.
While visiting the Lincoln Memorial, the World War II memorial (incorporated in 2004 for a war that does not happen in this series) is visible in the background.
British soldier Billy Murphy, when asked where he acquired a healthy understanding of electronics, replied it was at the University of Warwick. This would have been some feat, as U of Warwick wasn't established until 1965.
The sirens of the emergency vehicles heard in the background in Britain are those employed by British police, fire brigades and ambulances at least two decades after the Second World War ended (at the earliest in the late 1960s, but definitely in the '70s, '80s, and early '90s). During the 1940s, emergency vehicles used simple bells.
There is a Willys MB Jeep on the dock when Alvin boards the ship. These didn't go into production until July 1941 and were not exported to Britain until 1942. Furthermore, in "President Lindbergh's" world, they would not be in Britain at all.