ORIGINAL: Higg
I'm not sure about all red dot scopes, but the one im sure will not change POI by moving your head from one spot on the stock is the eotech (or bushnell holosight). A regular optic isnt going to make the gun more accurate, but make it easier to shoot smaller groups and hit with at longer ranges.
actually I have had the same problem as martinfaw is talking about with both the eotech and bushnell holosight hence they are basically the same sight probably made by the same manufacturer just marketed under 2 different names. any red dot scope primarily fuction similar to any optical sight including scopes. this problem... well not exactly a problem is more noticeable when mounted on pistols. the only red dot sight I have used that doesnt seem to be as effected is the doctor optics red dot sight but even with it if you move to much out of line with the sight you will have the same problem as you would with any other sight. just treat your red dot as if it were a scope at be consistant with your cheek weld position on the stock and you wont have any problems. good luck