The Ruger 10/22 is an amazing rifle. However, if there is one part on the Ruger 10/22 that needs improving, it is the sights. If you want to be kind, we can say the factory sights are of a poor design. If we want to be honest, the factory sights are terrible.
The rear sight has these little bitty small screws that the head will break in half. Shortly after I bought my Ruger 10/22 in 1986 I tried to adjust the rear sight for elevation. The head on the screw broke in half. This also happened to a buddy of mine. He bought his Ruger 10/22 shortly after I did, tried to adjust for elevation, screw head broke.
I do not know when it happened, but the other sight screw fell out. Good luck finding a replacement.
Even though the Ruger 10/22 is a great rifle, the factory sights leave a lot to be desired. To fix this problem I bought the TSR-200 Tech-sight for my rifle.