Combination guns, especially double barrels (both SxS and O/U) pretty often leave primers looking like that because the firing pins hit on an angle (and casehead/primer pushes back at an angle to the firing pin) This displaces material the primer is made from to one side. I have noticed it often but don't recall it causing much problem. When the primer striking at an angle does cause a problem, the problem is usually misfire/hangfires. This is especially prevalent with old guns that used .254" Berdan primers and currently available ammo uses .217" Berdan or .210 Boxer primers. Current ammo that uses .199"(small rifle) primers is not likely to have ever been originally made with .254" primers.
Mike