I've read about a similar issue on the GBO Tikka/Sako forum, he even sent it back to Beretta for repair, but it did no good, they returned it after 6 months /ubbthreads/images/graemlins/crazy.gif and it was still bad. He bought the Talley lightweight combo rings and all was well.
I decided to not use the Tikka rings, the screws really are pitiful and didn't want to waste my time, have researched the Talleys and no one had a complaint, so I went with them, with the Nikon Omega 3-9x40 scope reticle mechanically centered, and mounted in lapped low rings, I only had to adjust the horizontal turret 6 clicks to be dead center on a lazer bore sighter, so they're aligned to the bore better than any ring I've ever mounted, they use the 4 mounting holes in the receiver, not the dovetail. /ubbthreads/images/graemlins/grinning-smiley-003.gif
http://www.talleyrings.com/lightweight.php
http://www.swfa.com/c-943-tikka.aspx
