In the murder trial, Police Sgt. Dillings testifies that he saw Gridley and Hardwicke standing together with their arms around each other, and that she had the gun in her left hand. In the first scene flashback, they are standing together and her right hand is down along her side with the gun in it. In her flashback scene later, she has the gun in her left hand after Miles is shot.
Bill says "Well, in Saudi Arabia you have a choice, drinking scotch or drilling for oil." Alcohol was made illegal in Saudi Arabia in 1952. However Bill worked for the American embassy in Saudi Arabia and probably lived in a compound set aside for foreigners where the no-alcohol law would not be enforced.
When Jake Lemmon's character runs up the stairs to confront Kim Novak's character after the trial (at app. 1 hr. 20 min), he brushes his left hand across the square column on the landing and the obviously wet stain or paint smears.
Gridley has just transferred to London from Saudi Arabia. When Gridley first meets Ambruster, Ambruster says "I understand you've been in Saudi Arabia. I was there myself once." Later, Ambruster says to Gridley "If you foul up, Gridley, I'll have you back in the Sahara so fast you'll think London was only a mirage." The Sahara is not located in Saudi Arabia.