In episode five, the crew are in Monaco for the 1963 Monaco Grand Prix. The actual race was held on May 26, 1963, one month before JFK's famous Berlin speech (June 26, 1963)which was shown two episodes prior to this one (Ich Bin Ein Berliner, #1.3).
When the Pan Am Boeing 707 is shown on what appears to be about a five mile final approach to landing at the Nice airport, the landing gear is down, but no flaps or slats are extended. The aircraft would be fully configured for landing by at least five miles out, at the final approach fix, with the gear down and full flaps. The aircraft's stall speed without flaps and slats (Leading Edge Devices that help generate a great amount of lift at low speeds) would be so high the aircraft couldn't touch down slowly enough to stop on almost any civilian runway.
The stewardesses admire a supposedly expensive dress that costs 700 Francs. But at the time, 700 French Francs was only equivalent to $1.43 (US).
In the episode, Colette comments about it being July. That year, the Monaco Grand Prix actually took place on May 26, 1963.
There is a flight from London to Monte Carlo, then they are shown flying into Nice, France. Monte Carlo has no airport of it's own. Monaco is served via Nice airport.
During the IND Subway ride on the R-11, the background track plays a two-tone ring before the doors of the subway close. This two-tone ring sound was introduced with the R44 trains, which didn't enter service until 1971. Prior to that, there was simply a verbal notification that the doors were about to close.
When Ginny pulls up in the red sports car in Monaco and says "Want to go for a ride?", you can see the reflection of a boom mic come in from left to right on the left fender.