Fred Thursday is seen outside the railings of Buckingham Palace. A shot of Win filming him with a cine camera is followed by footage that she was shooting. However the position of the gatepost behind Fred is inconsistent with the position where we have just seen Win.
The opening scene is specifically set in September of 1962, but the radio in Laxman's car is heard giving a news broadcast about the Cuban Missile Crisis of that year. The crisis was in fact, spread over thirteen days in the second half of October and at the beginning of November. Also, the newsreader mispronounces the name of the Russian Foreign Minister as "Gromko" - it should have been "Grow-MEE-ko".
Is that how Londoners think Nebraskans speak? Both characters have atrocious accents more Welsh than American. And clearly not from Omaha.
The British actress playing the American wife (Mrs. Levin) does a poor job, unusual for this series. It's an accent in word only, lacking the accurate pitch, timbre or cadence. The actor playing her husband gets it right.