First thing I would do is measure the rifling twist with a cleaning rod like several folks suggested.
If it is in fact 1/10, it should shoot 117 grain flat base semi-pointed bullets just fine.
(If it is slower then 1/10, somebody put a slower twist 1/12 barrel on it for a varmint rig shooting light 60-75 grain bullets.)
Next, I would slug the bore and make sure it is in fact a .257" barrel.
(It would keyhole real bad if it happens to be a .264", or .270" barrel some jack-leg chambered for .257 Roberts by mistake.)
Other then that, crown damage, or lathe live-center damage to the muzzle is about the only other thing it can be.
BTW: It has nothing to do with break-in.
A new barrel should not be shooting bullets sideways at 50 yards, break-in or no break-in.
rc