Assuming you are asking for "advice for new shooters"
... and my apologies if you weren't, because I don't mean to seem condescending...
Some common mistakes I see at the range:
1) Shooting from an unbalanced or uncomfortable posture. This could include feet placed in too narrow a stance; leaning backward to counter-balance the weight of the pistol; and any number of other things.
I usually recommend either a Weaver or an Isosceles stance. Both are actually modified versions of martial arts stances. The Weaver is very much like a karate "front stance." The Isosceles closely resembles a "horse stance."
Each stance has advantages and disadvantages when it comes to movement, engaging targets to the side, etc, but we'll leave the differences aside for now.
What either stance has in common is a balanced posture, either both knees or forward knee somewhat bent, allowing a slight forward crouch while maintaining a stable, balanced pistol. The slightly forward crouch helps absorb recoil (whereas leaning back to balance the gun can have negative effects during recoil).
What both stances also have in common, once you get used to them, is that you use your hands and the sights to fine-tune your aim, but your body position (feet, hips, etc) actually initiates the gross aim, IE if you learn the body positions, you'll bring your weapon up more or less pointing at the target before you ever look at the sights.
2) Bad trigger finger position. This could be caused by poor form or lack of form, but it could also be caused by a weapon that just doesn't fit the shooter's hand all that well. (Note: part of the weapon selection process should be finding a gun that is comfortable to hold, and that allows you to use the first pad, or first joint of your trigger finger without inducing cramps or contortions.)
For single action trigger pull, you ideally want your first pad on the trigger. For double action trigger pull, you want the first joint. (Some people do either/or and their technique works for them, but these are usually the recommended positions.) Putting your finger too deep into the trigger will typically result in pushing the gun to the left for a RH shooter, and right for an LH shooter.
3) Pulling vs squeezing. The trigger should be smoothly squeezed, not roughly jerked. Think of it kind of like driving a stick shift, with the trigger as the clutch. Unless you want to squeal the tires and burn out, you'd normally ease the clutch in. Kind of the same deal with the trigger.
4a) Not focusing on the front sight. Order of priority of focus should be: front sight, target, rear sight. Front sight should be maintained on the target throughout the trigger pull, in much the same way that one should focus on the cue ball all the way through an 8ball cue stroke. In 8ball, if you take your eye off the target, you tend to jerk the cue stick up and top spin or shunt off the cue ball. In shooting, if you lose front sight focus, you may tend to pull the gun off target in the last part of the stroke.
4b) Not focusing on follow-through. If you think about bringing your sights smoothly back on target from recoil (emphasis on "smoothly"), it facilitates focus on the front sight.
5) As noted by a previous poster, lack of breath control. You want to engage the trigger on the nulls in between breaths, not while your rib cage and diaphragm are actively inflating or deflating. Why? Goes back to the "stable platform" concept.
6) Poor grip technique. A good grip should have the hand high on the grip-frame, to minimize bore axis height over the hand, and to facilitate always getting the same grip. (Note: make sure the weapon you select is not noted for hammer-bite or slide-bite.) The hand should hold the weapon firmly,but should not white-knuckle. If using a two-hand technique, the primary hand should be in such a position that it could shoot the gun completely unsupported. The support hand is a bonus, not a necessity.
7) Speaking of two-handed grips - don't fight with yourself. The support hand should pull back slightly, as the primary hand pushes into the support hand - but only enough to create just enough dynamic tension to stabilize the gun. If you start doing plyometric exercises, your hands will start shaking, and accuracy goes out the window.
Cheers,
M