On the subject of nuclear errors, I'm currently reading Richard Rhodes
The Making of the Atomic Bomb, which is fascinating. I've got to the part where the Nazis have kicked out all the Jewish nuclear scientists, thus depriving Nazi Germany of an invaluable pool of knowledge while simultaneously handing the atomic bomb over the United States. If there's ever an argument against racial nationalism, there it is.
But that's not my suggestion. I'm sure "what if the Nazis hadn't been anti-semitic" has been done to death. In 1954 the US conducted the Castle Bravo nuclear test. The plan was to detonate a 6mt bomb over Bikini Atoll, but due to a miscalculation the explosive yield was actually 15mt. Something about the lithium casing in the bomb. Imagine producing 9mt of energy by accident! I learn from Wikipedia's article on the Trinity test that there was some guesswork involved as to the explosive yield of the bomb, and:
"[New York Times reporter William Laurence] had prepared four releases, covering outcomes ranging from an account of a successful test (the one which was used) to catastrophic scenarios involving serious damage to surrounding communities, evacuation of nearby residents, and a placeholder for the names of those killed. As Laurence was a witness to the test he knew that the last release, if used, might be his own obituary."
The original plan was to encase the bomb in a large, thick metal vessel called Jumbo, so that if the explosion was a failure they could recover the plutonium. I wouldn't like to have that job. In the event Jumbo wasn't used, but suppose for handwavy technical reasons it increased the yield tenfold, purely by accident. What would be the results? Firstly all the measuring equipment would have been completely destroyed, rendering most of the test a failure; secondly a whole bunch of top nuclear scientists would have been blinded; as would thousands of civilians, including at least one nearby airline pilot; it would be impossible to maintain the veil of secrecy; by this time it didn't matter if the Japanese were aware of the bomb and the Soviets had spies, but the press would be running lottery competitions giving readers a chance to guess which Japanese city would be hit first, etc.