I notice that when I adjust shots, I would rotate the racket a little. Is that just a player preference or am I gripping the racket incorrectly?
What do you mean by "adjusting shots"? Certainly you need to adjust your grip to deal with different positions of the shuttle (e.g. in front of you vs. behind you). It's also often helpful to make subtle grip adjustments to help control the angle of the shot (more so in the midcourt and forecourt areas, and not as much in the rearcourt where a longer hitting action is generally used).