When you are sighting in, how are you resting the gun? Im not an expert but Ived owned and sighted in a few slug guns .The biggest mistake I see is guys make, is resting the pump handle on the front bag, this is not a stable rest, especially on the more wiggley pumps like 870s and mossbergs, you will get flyers. Im also amazed at the amount of people I see at the range, that dont even use a rear bag when sighing in
The best way Ive found to sightin a pump slug gun, is to rest the receiver(not the pump) on the front bag and pull down hard on the receiver w/ your left hand ,and back into your shoulder hard w/ your right hand(this is if you shoot righty) It might sound trivial, but I definatly found shooting form is critical when sjghting in pumps.
X2 on keeping the barrel nut tight, and mabye think about "pinning" (bolting) the barrel to the reciever if this is a dedicated slug gun, smiths supposedly charge around 50$
Ive also found that sabot slugs w/ thin walled sabots like lightfield, brennekee,hastings etc. give the least flyers. Good luck.