Technique #1: Par-cook potatoes before grilling for better control
It may seem like extra work, but I like to partially cook (by simmering) most potatoes before grilling them. Here's why: first, it cuts down on the final grilling time, so I can put the potatoes on just as I finish grilling the meat or whatever else I'm making. Since the potatoes are already mostly cooked, they only need to be seared over direct heat to create a golden brown crust. I'm mainly looking for visual clues to see when the potatoes are done, so I don't have to pay as much attention to them. I also don't have to cover the grill, so I can grill a steak at the same time. And if I'm entertaining, I can hand off the grilling to someone else, knowing they just have to look at the potatoes to know when they're done.
I especially like to use this method for dense-fleshed potatoes like Red Bliss and Yukon Gold. Grilled this way, they have almost the texture of french fries by the time they're done: golden on the outside, fluffy and cakey on the inside.
Simmer potato slices gently until just shy of fully cooked.
Add a simple coating of mustard and mayonnaise to keep the potatoes moist.