Yes, upgrade the scope. Remember, when you sight in your rifle, the first 3-5 shots after cleaning will "shoot in the barrel." You will have about 12-15 shots after that which are pretty accurate, then you need to clean it again. Same deal, then you have about 12-15 shots you can make that will hit where you sighted it in at.

Also, your first 2-3 shots after the barrel is shot in will be the most accurate if fired successively. After that the reciever and barrel will heat up and cause your pattern to become erratic for various reasons. Keep this in mind when sighting the gun in too, and wait 10-15 minutes between shots for the best results. A hot day may require more time between shots.

This is an over simplification, but I think that if you generally follow this advise you will be okay.