I have the same problem here with the sore knees. Mine I believe was due to some poor form and my knees would turn in a bit on the way out of the hole (I thought I was doing good till I really watched some vids of myself from front on), weak glute medius adding to the rotation of the knees as mentioned before (both diagnosed by a Physio) and to top it all off, high volume. In-fact I went from a max of 25-30 squats a week total as I only power cleaned power snatched, to hitting over 50 a day, if you include the start positions which are not squat depth but still pretty low for me, anyway.
The way to recovery, which by the way diagnosis was 2 weeks ago, was rest for 2 weeks. When standing, Glute Medius activation drills, clinch the butt checks while standing etc. and I have been doing some GHD raises and basically anything that gets the butt activated.
I started Squatting again 2 days ago, really working on getting the glutes to activate and knees over the toes. Took the day off yesterday and went at front squats today starting off cautiously, getting heavier for doubles and ended up setting a new PR! 4 hours later, Tired but no pain as yet.
Going to have a look at better programming with the coach.
Oh yeah don't forget the flexibility. It wasn't my issue as I am pretty darn flexible but, it was the first thing the Physio asked about