I'm always amused by the joke "Of course Kubrick faked the moon landing, but being a perfectionist was only willing to film on location", when in reality he was nothing of the sort. A lot of his filming locations were within an hours travel from home. I suppose it makes sense, even without the 3 month break, FMJ would have been 11 months of filming.

The most immersion breaking part of Dr Strangelove for me is always the outside shot of the ground assault on the "American" base which architecturally is so obviously British it snaps me out of the film each time.