Just looked at the first set here, Rob (http://startingstrength.com/resource...ad.php?t=50394).
You do need a bit more depth, hard to say exactly how much from that video - but we're not talking half squats here, yours are close and just need to be a little deeper. The other thing for you to work on right away is getting your knee position set by the time you're about half way down. This will help keep your knees happy and also prevent the hamstrings from slacking distally at the bottom and losing tightness. To initiate the squat think "knees and hips together," then when you're about halfway down, it's just hips and lean over. Push knees out the whole time. Let's see how that goes for you.