There are a few people I coach (no names mentioned!) that move their head as they hit the ball. A couple of these players are tall and get low too late and are dipping their head as they hit the ball. This is something that us shorter people don't have to worry about as much and is not the focus of this post.
Some people that are smaller in stature have another problem with their head moving as they are hitting the ball. This isn't just limited to people that are shorter or thin, but anyone this is trying to overhit the ball that their technique falls apart. Looking at some frame by frame video from beside the player you can watch at their head and shudders rotate along with their swing (not after contact). Besides not actually watching the ball as they hit it, opening up your shoulders before you contact the ball will decrease your consistency (especially on your straight drives and drops).
Similar to those that are trying to overhit the ball there are those that are too worried about getting back to the T that they also open up their shoulders too early and begin clearing before they actually contact the ball. This is a very fine line because the top players will look as if they are clearing before they hit, but the timing that they do this is the important part. If you watch a top player on video, frame by frame you will see their head is still and their shoulders don't open up as they contact the ball (besides for head and shoulder fakes!).
So what can you do if you are moving your head or opening up your shoulders before you hit the ball? Here are some exercises I do with my athletes. I start with basic feeding drills and ask that they keep their head down and hold their follow through until they hear the ball hit the front wall. This will be quite challenging in itself. Another visual tool that may help them watch the ball and keep their head still while hitting is ask the athlete to look for the yellow dots on the squash ball. Doing this focuses their attention onto the ball and ensures that they are watching and likely keeping their head still.
The main think to when doing these basic drills is to give them plenty of time to recover after they hit; you should start with no or very little pressure (depending on the athletes ability). Once they feel comfortable doing this, then you can try and speed things up a bit. I do the same thing but start putting them under a bit more pressure with the feeding. This makes it more difficult to get to the ball in a a balanced position. For example, if we were focusing on keeping their head still on the backhand drive I could do a drill such as this. I boast, they hit a forehand drive, I volley drop (not too good) and they hit the backhand straight drive while holding their follow through and keeping their head down until the ball hits the front wall. I don't volley their drive to give them time to do this before repeating again. As the player progresses make the drills more challenging and then record some more video to see if they have made the adjustment.
Obviously one cannot hold their follow through and keep their head still/down after they hit for a noticeably period of time in a match setting. But I guarantee that they will see the results in the drills. You will need to focus on this for a significant amount of time to permanently change/learn the skill. I also recommend avoiding the temptation to hit the ball as hard as you can. Just like in golf if you put everything into it likely your technique will not hold up and your ball will not go where you want it. After all if your drives and drops are that much tighter you can afford losing a couple of miles per hours and the smallest fraction of a second of recovery! If you don't believe me watch the top pros carefully..no smash and dash hackers (or technically dash before they bash) players on the tour! Accuracy and power is great, but if I would give up a little power for improved accuracy. Look at golf, I don't see any of the world long drive competitors making a living on the PGA or LPGA tours!!