Continuity: When Pyle is coming to visit Fowler in his apartment for the final time, his dog supposedly leaves a footprint in wet cement which is a clue for the detective. In the scene shown, the dog never touches the cement (his paw lands on a nearby tile).
Crew or equipment visible: When Fowler and his assistant are riding in the car through a crowd, a crewmember pushing the camera is visible just below Fowler's arm.
Errors made by characters (possibly deliberate errors by the filmmakers): Alden shows Phuong a picture of Fanueuil Hall in Boston and says, "This is Fanway Hall". Sounds like Fenway Hall. Bostonians say 'Fanyel" hall, or less often, 'Fan-you-well' hall. Fenway Park is where the Red Sox play, so named because is is near the Fens, a marshy area off the Charles river. Fenway has nothing to do with Faneuil.
Errors in geography: When Fowler is reading his report of the massacre in The Times, the text says "120 kilometers". In the unlikely event that an English journalist in the 1950s would use kilometers instead of miles, he would have spelled it "kilometres". Also, the text reads that Phat Diem is "120 kilometers north of Hanoi" when, in fact, it is 120 kilometers SOUTH of Hanoi.
Errors made by characters (possibly deliberate errors by the filmmakers): Fowler constantly mispronounces Phuong's name (as "phong" instead of "phuong"), even though he had been partnered to her for two years. Phuong corrected Pyle when he made the same mistake.
Anachronisms: Before the end titles, we are treated to headlines in The Times from the 1950s, over Fowler's byline. The variant "advisor" is seen instead of the more traditional "adviser", which was (and still is) prescribed by The Times' style guide - although "advisor" had occasionally appeared since at least 1833.