Nutzo,
First I want to welcome you to the best darn firearms forum on the internet.
I shot expert in the USMC with the M16
Apples and oranges, no, let me rephrase that... Apples and Carrots. While some of the principles are the same (sight alinement, sight picture, trigger press) the shooting of the two is fundimentally direrent.
With a pistol there are more things that need to be practiced. Stance and grip being the biggest. Now, also remember that with a handgun you are holding it out there with two hand at arm length, trying to keep the sights alined on the target and then moving the trigger towards the rear. Until you have practice this your "hold" will be shakey.
Also, you may want to change where your trigger finger is falling (and pressing) on the trigger. If you use the very tip of your finger it can cause you to "push" the entire weapon one way as you go through your draw stroke. If you put too much finger in there it can cause you to "pull" the entire weapon. Either way you can shoot good groups but be off zero consistantly.
I would suggest doing some dry firing at a target
(Ensure there is no ammo in the weapon nor in the room itself). Start off with a normal trigger pull and watch your front sight to see if it moves a cetain way. If it does try adjusting you finger on the trigger. If you front sight stays centered in the rear and your target aiming point doesn't change than all you need to do then is keep dry firing.
Remember Boot Camp? The week before you shot on the Range for score? What were you doing?
Dry Firing of course. This builds up the muscles that your using so that you have a smoother trigger transition. The smoother your trigger press (notice I said press, not pull nor push) the less your weapon will move during it.
Never forget.
Front Sight..... P... R... E... S... S...