Factual error: When the B-52 is flying low over Russia, the shadow on the ground is a Boeing B-17G, a World War II propeller driven bomber.
Factual error: After the B-52 has been hit by the missile it's supposed to leak fuel at a rather high rate. Such a leak would cause a visible trail, however, we only see some black smoke right after the hit which disappears after the fires are extinguished. (01:01:55)
Factual error: When Major Kong is riding the bomb down like a horse, there is absolutely no wind whatsoever. Not only do we not hear it, but we can also not see any wind effects on Major Kong, as he can be heard to yell and holler quite clearly, and he is waving his hat like there is no danger of it blowing out of his hand.
Factual error: In the scene outside the where they U.S. Army soldiers are attacking the Generals headquarters, you see one American soldier firing at the headquarters building using a WWII era German Army MP40 Schmeisser submachine gun. Although not uncommon for American solders during WWII to use captured enemy weapons in a tight situation, it certainly would not be issued or allowed in the stateside peacetime early 1960's. Several soldiers are actually carrying and firing the U.S M3A1 "Grease Gun", but a few are doing the same with MP40s, presumably as a stand-in for the "Grease Gun".
Factual error: During the B-52's final destination bombing run the bombardier counts down the distance from target to the crew. The beginning distance starts at 10 miles from target down to 3 miles at the rate of 1 mile per minute or 60 mph. A B-52's minimum cruising speed is about 300 mph, which calculates to traveling a mile every 12 seconds. (01:17:10 - 01:22:50)
Answer: Peter Sellers improvised it. During that scene if you watch the actor playing the Russian character you can see him trying not to laugh at Seller's performance.