I got a service grade M1 from the CMP about a month ago, a Springfield with a serial number that puts it in 1952 and a SA 4-53 barrel. Had it out to the range twice so far, the first time with light, non-cycling loads that printed 10-shot groups from 3 to 4.5" at 100 yards. I shot these loads with a drilled out gas cylinder screw so there would be no "partial cycling."
Last time out I shot cycling loads in 8-shot groups. Some groups strung vertically and some horizontally. Clue: I was cranking the sights around so I could place multiple groups on the large, MR-31 targets. I wasn't really putting 2 and 2 together until I got near the end, and shot a "group" that was actually two 4-shot groups, each about 2", 4-1/2" apart diagonally.
The best group happened to be fired without a sight change, shooting on a different target. It was a nice 1.88" cluster fired with the Lee 312-185 cast of 50-50 WW and lead, heat treated, LBT Blue lube, 40 grs. of H4831SC, a 3/4 gr. tuft of Dacron and a 1/16" LDPE wad. This bore is lightly pitted, and the LDPE wads seem to help prevent leading. I got some leading the first time out with the light loads and no wads. These cycling loads did not lead.
I suspect something wrong with the rear sight, but I'll defer to the experts. It seems to be tight enough, as the aperture cannot be pushed down with the thumb when 2 clicks below the top of adjustment, and the windage does not adjust easily. The aperture has a very small amount of side-to-side movement, but I put an indicator on it and got about .005" movement. That should equate to less than 3/4" at 100 yards. The trigger guard seems to pull the receiver into the stock snugly. There is no perceptible fore and aft movement of the receiver in the stock with the trigger housing removed.