The inherent accuracy is going to be better than most shooters can practically realize. It's the shooter that's realistically going to "limit" the potential for accuracy with the little 5-shot guns.
Even a number of skilled revolver shooters accustomed to shooting larger revolvers sometimes experience difficulty in shooting the diminutive snubs.
The very attributes which make the little guns so attractive for their intended purpose often are potential disadvantages for many shooters. Small grip, long & heavy DA trigger, different trigger reach (and therefore "leverage",) rudimentary sights (and harder to see with the older models having the thinner notches and front blades), lighter weight (so more felt recoil), etc.
They can still exhibit some great accuracy for a trained & skilled revolver shooter, though. They even have occasional snub matches where competitors make good shots from some impressive distances, like at 50-60 yards.
FWIW, I usually find I can generally use my assorted J-frames (and some others which are either well-used & abused training guns or which belong to other folks) to get consistent hits on clothespins at 5 yards. It's all about trigger technique & control, which means investing time in continued practice once good revolver trigger technique has been learned on the smaller wheel guns.
Maybe seek out a skilled and experienced revolver shooter or instructor at a local range. Too many folks try to "stage" a revolver trigger during the DA trigger stroke, instead of making it a smooth and quick press while focusing on the sight (and follow-through).
One of my former partners decided to dig out his old model 36 a while back. It had apparently been more than 20 years since he'd carried and used it. Naturally, he was having initial trouble getting consistently accurate hits from 3-10 yards.
Once we reacquainted him with his previous revolver skills (from his service revolver days), and he spent a couple of range sessions working on remembering his DA revolver trigger technique, which had long since fallen into disuse, he started getting solid, well placed hits.
For him, the last thing that seemed necessary to restore his accuracy was getting him to remember to stop trying to "stage" the DA trigger, and just make it a smooth, even & quick press. He was actually pretty surprised by quickly & easily his groups tightened up once he got his trigger control "groove" back.
Got anybody around locally who could lend you some assistance in the way of developing & refining revolver skills regarding the little M60?