You would certainly hear something about an issue that arose out of an act of negligence during the planning phase, or not notifying a flight of a hazardous situation while enroute that compromised safety or caused a disruption in the operation. Otherwise, planes are gonna hit birds, get struck by lightning, divert due to weather/ATC holding, have medical emergencies, and many other irregular operations. Stuff happens.
As far as delays... There are so many departments, people, and variables involved in completing even one flight.
Ops
Ramp
Catering
Mx
ATC
Wx
Flight Crew
In Flight
Crew Sched
Dispatch
Mx Cntrl
Any one of the above can have a hiccup and cause a delay. I will say that dispatch does have to account for all of them and sometimes track them down, get clarification, and take any necessary steps to minimize any further delays if possible. Delays are going to happen. Dispatch is in the business of making things happen. Managers can argue delays in the morning with other managers and who ever else. We don't have time to dwell on them.
Angry Pilots? Nah, not really. Everyone can get a little flustered now and again, but angry doesn't do anyone any good. Everyone from the above listed departments (sure i'm missing some) is generally cool to deal with.
I think the fastest way to get "shut down" by the many different people spread all over the country or countries, would be to get straight up angry at them (sometimes you really really want to though) lol.