To clarify the previous posts a bit there are accuracy results that are EXTREMELY TYPICAL for those new to handguns or a particular platform.
One of these is for a right hander to shoot low and left and a left hander shooting low and right. If you are shooting shows this typical response you are having problems with the trigger. The "fix" for this is Practice and concentration on proper technique. Specifically slow down your firing rate, concentrate on relaxing fully through the trigger break, and use a slow steady trigger press WITHOUT ANTICIPATING the gun firing.
The second most comon problem is FLINCHING. BTW, don't even attempt trying to say you don't flinch, because anyone who's shot handguns for a long time knows darned well that everyone grows a flinch at some point. Personally I believe that the difference between a good handgun shooter and someone who shoots poorly is that the good shooters have learned how to feel it when they flinch and will slow down and practice for a good clean release until they conquer that flinch. Bottomline, centerfire handguns have enough recoil and muzzle blast to cause anyone to flinch, how you deal with it when you are flinching will determine how good a handgun shooter you'll become.
Finally, in closing I'll tell you that hanguns are so well made today that accuracy problems due to a defect is exremely rare. The simple truth is that 99% of the time accuracy probelms are caused by the shooter, not a defect in the gun. As for your better results with a 22 caliber pistol they have so little recoil or blast that anyone can shoot them without flinching. As for your success with that 357 Magnum, I have a pretty strong hunch that you were shooting in Single Action, which pretty much takes Trigger Management out of the picture.