There was one that might qualify. It happened the day before.
With the combination of tide and moon, June 5th and 6th offered the best chance of the month for the landing. If it didn't happen then, it possibly would have been delayed until July etc.
The weather on the 5th was not conducive to a seaborne invasion, but some met chap still had to make the call. In any event, you can't all set off at once, so a small flotilla was launched on the 5th. As the minutes ticked by, they finally had to face it that the invasion would have to be delayed until the 6th.
Apparently the flotilla was maintaining radio silence - and I have to say I don't understand why they couldn't have listened and not replied, but for some reason, they could not call them back by radio. In any event, if they were to continue, they would be alone, and apart from meeting certain death, they would also give away the element of surprise.
So it fell onto the shoulders of someone who's name I don't know to search the channel for the flotilla, and having found it (a feat in itself I would have thought) pass over the lead ship and drop a message in a tin can.
Fortunately his aim was good and the message was received and acted upon and the rest is history.
I'll try and see if I can get any more details, but to me it's only one part of one of the most fascinating stories of history. There were so many little things like that, the BIGOT documents, the Mulberry crossword, the depth of the FUSAG deception, the Hobart funnies that didn't quite work, the story of the commandoes on the beach taking sand and profile samples when the sentry walked past, the request for holiday snaps to help build a composite picture of the landing place, Von Runstead's wife's birthday falling on the 5th (or was it Rommel's wife?), the fact that when the invasion took place, the German high command were in the middle of an exersize to simulate an allied landing.
Sorry, I went on, but to me that has to be one of the best pieces of flying.