H-hour always seems to be on the hour in movies about WW1 and WW2. "We attack at 0600/0700". This seems odd. Surely times should vary at random? Is this how things were done? Couldn't the enemy simply stand easy until the big hand hit a minute to twelve and then rest again at two minutes past?

Attack/movement/directed start times were dictated by a variety of factors. In an OPORD (military for Operations Order) start times would be different for different parts of the overall operations: The air attack might be launched at H-30, the artillery attack at H-15, the first attack at 'H' and so on. Considering the complexity of the operation, commanders usually tried to make start times "H' as simple as possible to prevent confusion. I remember the really fun part of trying to synchronic watches. Nobody ever was on the exact same time.