I've been discussing this quite a bit over at AKFiles, one guy there was getting absolute crap accuracy out of his pistol that went from 5-7 moa out of the box down to 1.75-3 MOA with a mean of 2.25 after about 200 rounds
some rifles and pistols need a break in period
out of the box I was consistently shooting 2-3 moa 5 and 10 round groups at 100 yards with irons and astigmatism using Wolf Polyformance 123gr for 3 hours at the range a week or so ago, I guarantee it would have been even better with an optic and Hornady SST or some ammo that is better manufactured
Ammo plays a big factor in accuracy with the ACE, and really any 7.62x39mm
most guys with quality ammo are getting sub 2 moa close to 1 moa, with craptasterific ammo you'll be anywhere from 1.5-3 moa, if you're at 4 moa there's a problem, most likely not the gun
on the facebook IWI Galil ACE owner's page, the .308 version had a sub moa 10 round group at 200 yards