The squat is the one movement that is feared next to deadlifts and the one movement that's first at a meet. A good majority of powerlifters can squat close to what they can pull and sometimes that's a good gauge to see if your improving on squats or not. But here are some typical issues you may come across on the squat:
Trouble Locking Out - This is mostly typical of any beginning powerlifter. Nothing to freak out about really...LOL. To fix this, you would have to do some
good mornings (Wide-Stance or Close-Stance). This will help you get used to heavy weight on your back since your squatting position starting out is a good morning. Another way is to speed work for your squat. Westside Barbell advocates these by doing 10 sets of 2 with 30 second rest between sets. Once you get used to these, you can use bands and/or chains to strengthen your speed towards lockout but warning - your hips may be fried after doing that.
Trouble Going Below Parallel - I've had this problem with squats in the past and it's a pain in the ass too. This is usually caused by "tight" hips that stop you just short of going parallel and it usually takes heavy weight to make you go lower. I fixed this problem by squatting deep with light weight like 135 and/or 225 and did this for about 2-3 months on leg day.
Slow coming out of the Bottom - Some would say that this would deal with lockout power but it isn't - it's the explosion coming out of the bottom. Speed work on squats helps with this as well. You can't come out of the hole slow - you'll expend too much energy that way. Another way to deal with this issue, is to implement plyometrics.
Josh Bryant has some good info on this topic at his site: http://joshstrength.com. I've been doing plyometrics for a while now and its helps with exploding out of the bottom. Also, WSB believes in sled pulling to help with explosion out of the bottom. These work your hips like none other and it also works on GPP, which I'll explain later. You can find more info at http://elitefts.com.
Not used to Heavy Weight - This can be fixed with heavy good mornings, 3/4 squats, and walkouts. I had trouble with this earlier this year myself. When I got up to 500, I felt as if I couldn't handle the weight. That's changed now because I had to get myself used to heavier weights. When you get used to heavier weights, your mind can focus more on the lift itself. It becomes dangerous when you have more weight than you can handle or control.
Getting Tired Quick - This is what Louie Simmons would call "lack" of GPP- General Physical Preparedness. Let me explain: Two guys, one at 270 and the other at 305. Now automatically, you assume the 270 would be in more shape than the 305 right? Well, let's continue. They both decide to do stride jumps (a plyometric movement) for some GPP. They do 10 reps each.
The 305 lifter is able to breeze through the jumps w/o too much trouble but the 270 guy isn't used to it and struggles a bit. I may be exaggerating a tad, but the 270 lifter is lacking GPP. The 305 lifter is more in shape than the 270 guy, therefore when they squat, the 305 lifter will be able to do heavy weight w/o too much fatigue. I can testify to this now because when I go heavy on anything, it doesn't tire me out like it used to in the past.
Going heavy would exert you to the max and it's because I've implemented GPP into my training. Simmons has an article on this at http://elitefts.com if you want to read more about why GPP is important. Plyometrics, sled pulling, etc will help this and condition you for lifting heavy which counts. You'll get this on speed squats if you're a beginner. But doing the speed squats will improve GPP as well.