Is it possible that you are pulling the handgun down a little when you shoot? The M&P tends to have a really gritty trigger, and a long trigger take up.
I bought my M&P 40 about a year ago, and was having similar issues, I was missing really low and was having a hard time hitting anything. I have been shooting 1911s for many years and when I purchased the M&P, I was really shocked. I realizedIt was a combo of my technique and the trigger pull. I was used to the smooth 4 pound trigger on the 1911 that had very little take up. The stock M&P trigger is often very stiff, heavy (in some cases) gritty and it also had a lot of take up. I began practicing my technique by using snap caps, and making sure I was taking up the slack, and following through. Since the trigger was so heavy and gritty, I would often pull the pistol down unknowingly, I started seeing improvements, when I was practicing with snap caps, and my shots became straighter. After a few hundred rounds, my trigger smoothed out a bit, but I eventually had an APEX tactical duty/carry kit, as well as an apex AEK polymer trigger, this improved the trigger reset, and the overall smoothness of my trigger pull. I am now shooting very accurately with my M&P and am happy with the result.
Practice slow shooting with snap caps, and maybe try to balance a spent casing on the front sight. This will give you a good indication of which direction you are dipping your pistol if you are. I hope this helps