I don't shoot off benches, so I can't give you group sizes in inches. I do compete in various venues involving steel plates and milsurp rifles. I do know that out at 400 yards the accuracy starts to go south. In other words, I fire a good solid shot that I call and the bullet doesn't strike where I called the shot. This would probably fit right in with the design specification. If the mil-spec called for 4" at 100 yards, you figure that best case, it might shoot 16" at 400 yards.
That is with a service grade Greek H&R.
Using a commercial Springfield Armory rifle I have gone five for five at 700 yards. The above mentioned CMP rifle isn't up to that.
Contrary to a lot of internet rumor from those who don't own one, the M1 rifle is not a super accruate tack driver. That spec of 4" at 100 yards is a lot closer to the truth the vast majority of the time. In order to make an M1 shoot about as good as a run of the mill commercial bolt action rifle that you buy at Wal-Mart takes a pretty good chunk of change. For confirmation on this, do an internet search for gunsmiths that do accuracy work on M1 rifles. See just how much you have to pay to get an accuracy job guarenteed to shoot 1" at 100 yards. I will give you a hint: the numbers are four figured.
I own four M1 rifles and really enjoy the crap out of them. I shoot them quite a bit. But, I am realistic about them and I don't try to make them something they are not. If I want a one hole, target rifle, I will start with something else. If I want a milsurp rifle with tons of history behind it, the M1 is my pick.