At 37 minutes, the injured Philip starts to button his shirt, but the collar is one button higher on the left than the right. When the camera cuts to another angle the buttons are now aligned.
During the early part of the movie (time stamp 3:19) a three vehicle convoy drive to a gate where in the background there is a parked military vehicle. But it is not Soviet made vehicle but belonging to the Swedish Army. It is Volvo C300/ L3314 series off-road 4-wheel light truck mainly used by the Swedish Army. It was sold to Netherlands, Saudi Arabia and Norway. Finnish Army had also some trucks. It was never sold to Russia and was never in use there.
The Admiral is driven home by going east down Whitehall towards Trafalgar Square, though he actually lives in on the Middlesex side of the Thames by Kew railway bridge, as is clear from the name of the adjacent sailing club. But in fact you would never go to Kew by crossing to the south side of the Thames at Westminster, but would indeed travel north (not east) on Whitehall to Trafalgar Square and turn west onto the A4, a much more direct route, crossing the Thames much closer to Kew itself.
When Kimberly is listening to the news broadcast of his "death", the newscaster refers to the Manhattan Project spy Ethel Rosenberg as Esther Rosenberg.
When Sir Gerald Scaith (Laurence Olivier) talks about the legalisation of homosexuality, he says that the law "would have saved Vassall, Maclean and Burgess," meaning John Vassall, Donald Maclean and Guy Burgess. The implication is that all three had betrayed their country because of fear of exposure as homosexuals, which was still illegal prior to 1967. However it's only really true of Vassall. Burgess and Maclean worked for the Soviet Union through conviction.