The 760 and 7600 are very accurate, due mostly to a free-floated barrel. The older rifles had the forend hanging off the barrel and were not as accurate, though passable.
Most 7600s will shoot close to MOA, but extraction of tight cases, mostly reloads, is not as strong as bolt actions. They're mostly used by people who use pump shotguns. Others with less experience with pumps don't tend to cycle the action under stressful situations (like buck fever).
The biggest "problem" I have with them is that the pump handle, by necessity, is fairly loose and rattles a bit. The other thing I don't like about the design (including 7400s) is that the sides of the receiver are flat and reflect the sun's rays, almost like a mirror.