When Philip goes into his mother's room, the close-up shot of the photo of himself on the table shows that the photo is to the left of the cross. In the next shot, the photo has moved to the right of the cross.
While the Royal family is watching the Apollo 11 lunar landing, the television is showing footage that was taken by a camera which was mounted inside the lunar modules right side window (where Buzz Aldrin was), showing the lunar surface getting closer and closer right up to the point of lunar touchdown. This film footage was not part of any live broadcast of the landing because it was not available until after the astronauts returned from the moon.
When meeting the astronauts, Prince Philip comments that they are sitting in the same positions as the Command Module. This is entirely incorrect. Armstrong is sitting in the Lunar Module Pilot's position, and Aldrin in the CM Pilot's launch position. Collins is sitting where he would sit only for splashdown.
The TV Prince Philip is watching the astronauts arrival at Buckingham Palace on, says Trinitron on the right but the picture tube is clearly not a Trinitron.
This episode takes place during the moon landings, in July of 1969. In one scene, kids can be seen bouncing through the room on orange space hoppers. Space hoppers were invented in 1971.
During a conversation with the Apollo 11 astronauts, Prince Philip mentions that his mother had recently died. Princess Alice died in December 1969, the astronauts visited Buckingham Palace in October 1969.
While watching pre-launch news about Apollo 11, a cake of the moon with a toy astronaut is brought in. The toy astronaut has red Commander Stripes on the legs of the space suit. The red stripes on the commanders suit were not used until 1970 with the Apollo 13 mission being the first to use them.