It's kinda hard to appreciate from the video, but it seems to me you are doing high bar, right? (With the bar on top of your traps).
With this type of squat there's less emphasis on driving with the hips, since much of the work is done by the quadriceps as the hamstrings slacken at the bottom and thus can't really help you rebound off the bottom.
The most important cue at the bottom for you in this case is to drive with your chest, not so much with your hips. You are basically trying to do low bar mechanics on a high bar position. That's why your squat looks so awkward. If you notice your bar path is almost like an S on the way up, making the lift much harder.
Watch this. Pay attention to the difference between low bar and high bar:
http://www.youtube.com/watch?v=cRMiUtscrHw
I'd drop the weight to 95lb and practice form with that
You are wrong and thus I'll correct you
It's absolutely okay for knees to go past the toes, specially on a high bar squat.
Notice how on the high bar squat the back angle is much more vertical. Thus the need have to travel forward to compensate. There's no way around that. How much the knees travel forward depends on the type of squat (the more vertical the back angle, the more they travel forward), stance (wider stance means less forward knees - check out a powerlifter's squat with a super ultra wide sumo stance: his shins will be pretty much vertical) and individual anthropometry (the longer the legs with respect to the torso, the more they'll travel forward).