I know that the Allied forces in World War 2 were able to decipher the German and Japanese radio codes with the help of a stolen Enigma computer. What other interesting secrets were keep from the public during World War two but reveled for years to come?
Tl;dr: The UK and US accidentally gassed an Italian harbor town and kept mum about it for decades.
Basic story is this: An American liberty ship called the John Harvey had been loaded with a secret cargo of mustard gas bombs, and sent to Bari, Italy. The mustard gas was not supposed to be used, but was stored there for use in a retaliatory strike if the Germans used poison gas first.
On December 23 December 2, 1943, a Luftwaffe raid on the town destroyed several ships. One of those ships was the John Harvey, and as the ship went down, the sulfur mustard leaked out of the shells into the surrounding water. This was not good for the sailors in the water, many of whom ended up coated in the stuff. And some mustard vaporized in the heat of the flames and entered the atmosphere, "gassing" a wider area.
About a day later, people start showing up at hospitals with chemical burns, blindness, and the like, but nobody knew about the mustard gas (though some suspected) and at least 85 people died as a result. Probably more, since we don't have good info on civillian casualties.
All of this was covered up until the 60s. The British didn't admit it had happened until the mid 80s.
source: Day of Battle, Rick Atkinson.
edit: got the date wrong.
While not actively hidden, the 1944 Exercise Tiger comes to mind. An Allied convoy was practicing maneuvers for the invasion coming that spring. The escorts given to the convoy were old and on different radio frequencies. A German E boat found the convoy, attacked, and darted back into the night. Almost a thousand American servicemen were killed and 2 LSTs were sunk and 2 other LSTs were seriously damaged. The families of those killed weren't notified until after the June invasion. While some reports of the disaster appeared that summer and in books in 1946, it really wasn't covered in depth. So while not actively hidden, it became forgotten by much of the public.
A couple good sources on this are Ken Small's The Forgotten Dead and the Invasion Before Normandy by Edwin Hoyt.
The Normandy invasion - amazing how they positioned all that manpower and equipment and no critical information was leaked - impossible to imagine a repeat of that success today.
The Manhattan Project was a well kept secret.