Better players tend to have stronger grips, with the left hand rotated farther away from the target. But for a lofted pitch, a weaker grip works better. Try taking your setup, then putting the back of your left hand against your left thigh and taking your grip again. When you re-grip, you won't turn your left hand way over the club, so you'll set a weaker grip -- and hit higher, softer pitches.
The way you position your eyes has a lot to do with how solidly you hit your chips. Your eye line should be set in two planes: parallel to the target line and level with the ground. If your eye line points left or right or one eye is higher than the other, your contact will suffer. Practice chipping wearing sunglasses: Once you get set over the ball, carefully take off the glasses and check your eye line.
On long bunker shots, say 30 or 40 yards, a shallow swing arc works better than a steep one, which requires a very precise entry into the sand. Think of this swing as a miniature hook shot. Aim right, sweep the club around your body on a flatter arc going back, and then try to pick the ball off the sand, swinging the club around you to the finish. At impact, think Turn the right palm to the ground.
Many good players miss right-to-left breaking putts on the low side. Buy yourself a little insurance on the high side with this tip I got from Raymond Floyd: Play the ball back an inch in your stance and more toward the toe of the putterhead, and set more weight on your left side. These moves combine to keep the face open longer so the ball will start right and stay on the high side.