Mine shoots to the left as well.
I've shot bullseye competition way back in the day, was on a competitive shooting team, yada, yada. True expereince teaches you the first thing to look at is yourself.
A gun shooting to the left is pretty common for a right hander, indicating trigger control, and concentrating on the trigger may yeild some positive results.
Of course the sights could be off too. I've shot enough M&P's, and own four now, and the sights being off aren't really out of the question either.
My Compact hit to the right. The front sight was indeed off. I moved it and it shoots dead on now. The Shield's grip and trigger are sufficiently different that I want a few more rounds out of mine before moving the sights. I still recognize that it may well be me. If I decide the sights need to be moved, I'll move them.
Think of it this way: As long as you are doing everything exactly the same, you will get the same result. If you keep getting the same result, and several other people do as well, there's no problem with moving the sights.
Shoot it enough that you're satisfied it's not you. If the rounds are still hitting in the same place, then just move the sights.