Continuity mistake: Patricia Neal is in flats as she runs across the field to give Gort the message. When Gort picks her up, she's in heels.
Character mistake: At the beginning of the film, the British radar-man says it's moving at 4,000 mph. Then says it must be a Buzzbomb. As a British radar man, he'd know that the Buzzbomb, or V1 rocket, only flew at 360 mph - 75% were shot down by the RAF.
Answer: They said, how they handle their earth problems is no concern to them, it's only if they bring it to outer space and other worlds, they would take drastic measures to ensure that did not happen.