Its key flaw is that you get a lot of bright people in a room with too much time on their hands and not enough interaction with others. So the American general staff, for example,
War Plan Red was actually designed for a war with England. In the late 1920s, American military strategists developed plans for a war with Japan (code name Orange), Germany (Black), Mexico (Green) and England (Red). The Americans imagined a conflict between the United States (Blue) and England over international trade: "The war aim of RED in a war with BLUE is conceived to be the definite elimination of BLUE as an important economic and commercial rival."
In the event of war, the American planners figured that England would use Canada (Crimson) -- then a quasi-pseudo-semi-independent British dominion -- as a launching pad for "a direct invasion of BLUE territory." That invasion might come overland, with British and Canadian troops attacking Buffalo, Detroit and Albany. Or it might come by sea, with amphibious landings on various American beaches -- including Rehoboth and Ocean City, both of which were identified by the planners as "excellent" sites for a Brit beachhead.
The plans are copiable for $0.15/page in the archives. I think they'd make good prank material.