Alwyn Cosgrove discusses the difference between mobility and stability, and how to spot them.  Notably, he looks at two pics of an overhead squat, one where the dude has decent form, and another where the dude doesn’t.  It LOOKS like a mobility problem, but when they get into the same position while lying on the ground, they can both mimic the overhead squat form. 

So the difference in squat form and depth was not a mobility issue – it was a stability
issue. Essentially the body is shutting down the range of motion – not
because of tightness or a restriction – but because it perceives a
threat due to the lack of stability.

…

Conclusion – a range of motion deficit or asymmetry may not be related
to tissue length or tension at all. It could be related to core
stability.

Mighty Kat, a fellow Oregon Olympic Weightlifter (and current state champion in her weight class), has an article up at Weightlifting Exchange entitled, “Six Tips for the Overhead Squat.”

The overhead squat is a pain in the ass, literally!  But, it’s the first exercise that I tend to have people do in the gym.  I give them a stick, do a demonstration, then have them try and “repeat after me”.  I can learn a lot about where a person’s current level of fitness is by how well they are able to perform this exercise.

If they let the bar drift too far forward, or if their arms remain bent throughout, then I know they have shoulder flexibility issues.  If they let their heels come up off the floor, then I know they have ankle and calf flexibility issues.  Some times people will literally shake while performing an overhead squat.  This can be from a number of causes, but foremost among them is a lack of stability strength and balance.

You can find a ton of other writing by Mighty Kat at her website, www.MightyKat.net, and at her blog, mightymix.blogspot.com/