Gotta ditto the guys - you have to double check each and every mounting screw, nut, etc. Also, I've had scopes that required a shot or a good knock to "settle" after adjustment. I just give it a good rap with whatever suitable I have on hand, but I've seen guys at the range with little rubber reflex hammer kind of things (like docs use). You adjust and knock it before you shoot. If you don't, the first shot out the barrel won't be to the same impact point as the next because the first shot settles the scope to where you adjusted it. If your scope is doing this and if you don't know about it, you can get odd groups and also chase the zero all over the target.

What kind of scope? I've had top quality and medium quality scopes and haven't found that makes a difference in accuracy - more in the area of sharpness, brightness etc. Good luck and let us know what you find.