I was using a Winchester Defender with a bead sight and was amazed that I could hit a human-shaped target with any accuracy 25+ yards away. After that, I upgraded to a Benelli M-1 with ghost ring sights and have no trouble putting big holes in the "A" zone on a regular basis.
I rarely carry a shotgun at work (carry a carbine instead), but I qual every quarter with an 870. This includes shooting slugs at 25 yards. I can easily put five slugs in the left side of the face (aiming at the left eye) with any rack grade 870s I've shot. A shotgun with decent sights and a slug is a fairly accurate weapon at reasonable ranges. Headshots are definitely possible at even longer ranges.
The purpose of a slug? Putting a very big hole in someone who needs lead therapy.