Two things that affect the point of impact with a shotgun are the fit of the stock to the shooter and how well the barrels are regulated. Building a S X S shotgun that works well is an expensive and time-consuming operation. Honestly, with a $430 s x s, if it shoots every time you pull the trigger and the only things wrong are what you describe, I think you did okay. The trigger might smooth out with use. My guess is, if you return it to Stoeger, and if they do anything about it, they will just send you another one and hope for the best.
