This gun should easily shoot three inch groups at 25yd. with good ammo and POA should not be off by that much if you know how to adjust the rear sight. (move it the same way you want the bullet to go) That is not a flame...just a FYI.
I suspect something else...like a bent front sight, or a cracked frame rail, etc. is causing this IF it is mechanical. Have you tried letting someone else shoot it? If you are "cross eye dominant" that could be an issue if you are switching eyes when shooting...but it is usually intermittent, not constant. The Glock's trigger action is different from the other guns for sure, so maybethat is a problem as well?
Diagnosing this stuff over the intertnet is almost impossible. Try placing a little more finger on the Glock trigger and sort of "ooching" (technical term...Ha!) it off of the sear rather than using the center of the tip of the finger as with a 1911, etc. and see if that helps.
The slightly shorter barrel is not the problem. If all else fails, you might send it back to Glock to be checked...for sure if it has less that 100,000 rounds through it, it ain't worn out!
Good luck