I'm reasonably sure that your gun will shoot better than 3" to 4" at 50 yards, at least with 357's. Like Chuck said, I think you'll do better once you're used to the trigger on it.
As far as the 38's shifting to the side, yes, it definately happens with some 357 lever actions regardless of the maker. I was blessed with my current 1894C because it shows no noticable horizontal shift at all regardless of the loads from very mild 38 velocities to full house 357 magnum loads.
My last 1894C shifted about 4" to 5" to the left at 75 yards when I switched to 38 specials which is a pain when fooling with a drift sight set up. I've since seen a couple more Marlins, a couple Winchesters, and one Rossi that showed similar results, all chambered in 357 magnum.
I think maybe the actions are torquing differently at different pressure levels which causes this to happen. I'm guessing that some rifles aren't fitted just right, or maybe a little loose tolerances or something.