The biggest dilemma in rock drilling is when you encounter 2 slightly different pore pressures within 2 layers of formation in 1 hole section: you'll a well kick when you lower your mud weight, but you will have a lost circulation when you raise it. One of the solution is by using an MPD (Managed Pressure Drilling) system.
The major dilemma for drilling is to be able to direct the head of the drill, and that depending on the geology encountered that the drill stem is resistant and that drilling can continue for several kilometers. The most important is the problem of drilling depth.