Last night I watched The Mouse that Roared. This is a political farce featuring a doomsday weapon and Peter Sellers in three separate roles, and almost certainly wouldn't be the first movie you think of based on that description. There's a reason for that, although in all fairness this one came first.
In brief summation, the Duchy of Fenwick's economy is based on the export of a distinctive kind of wine. California has started producing a knockoff, messing up the racket. The prime-minister has the idea of invading the US, starting a war, and losing it, in the belief that losing a war to America is the key to prosperity. (Based on a rather oversimplified history of postwar Germany, no doubt.) The plan is complicated by the fact that the US has evacuated the East Coast due to the testing of a new super-powerful bomb. When the invasion force arrives in New York there's no one to surrender to, and they inadvertently end up winning.
There are a few problems here. The nuclear scientist's daughter, played by Jean Seberg, has to fall in love with the invasion leader, one of the characters played by Sellers, when he takes her and her hostage as hostages. This romance is unmotivated at best, kind of unfortunate at worst. And while director Jack Arnold had quite a few films under his belt, including The Incredible Shrinking Man, let's just say he's no Stanley Kubrick. There's a lot of meandering in the movie, during which the comedy goes flat.
Still, points for being ahead of the curve in some ways. There's a good cast here too, including William Hartnell a few years before Doctor Who and Leo McKern a number of years before Rumpole of the Bailey.