I've shot a bunch with .223/5.56. Works fine. Here is is one from a couple of weeks ago with Barnes TSX 70 gr. bullets at 125 yards. It was a 150 lb. sow. Blasted through the vertebral column just behind the head and deflected out of the front of the neck (hence the muzzle blood).
Aim small, hit small. I was about 1.5" off my intended impact point closer to the base and behind the ear, but that error in any direction would still have dropped the pig via CNS trauma. The pig was stationary at the time of the shot, apparently watching a small group of deer it (and it's sounder) had driven away from a feeder.
A smoothbore Rem 870 (as in the suggested used police gun) will be best inside 50 yards, though no doubt you can shoot them further. Depending on the ammo, you might get 4 MOA and probably more like 5 or 6 MOA at 100 yards. With poor slugs (for your gun), up to 7-8 MOA.
With a rifled bore and slugs, you should get much better accuracy.
"If you look through your scope and see your shoe, aim higher."
-- said to me by my 11 year old daughter before going out for hogs 8/13/2011