How did people synchronize timekeeping during operations? For most things it sounds like precise time didn't matter all that much, but for the artillery units, they often have very specific firings schedules listed down to the minute. Would this have been coordinated over phone/telegraph? I can see all sorts of horrible things happening if some artillery commander's watch was slow and they didn't realize...
All sorts of horrible things did happen - infantry being killed by their own artillery happened a lot.
If you find some of the orders relating to the operations, they normally stipulate somewhere how the time is synchronised. What seems to be the way is that a central location - often divisional or brigade headquarters - specifies the 'master' time and each unit is responsible prior to the operation for sending an officer to HQ to synchronise their watch with the 'master' time. They would then return to their unit and everyone who needed to would synchronise their watch with them. It's sensible but it's far from foolproof.