I have two used mossberg 590 shotguns with the annoying habit of wiggling to safety ON when I rack the slide.

    Is this common ?/easily fixed ?  The screw is tight. I'm thinking there is a loose or worn out detent or something. The guns are in otherwise excellent condition.

yes this is a problem I had

What is happening is that the rear of the firing pin is hitting the downward tang or the screw that holds that saftey together.   I would suggest to gut your 590 and see if the saftey is installed correctly or if there is a screw hanging down inside that saftey cresent.

that cresent needs to be clear for the firing pin to slide back and not disturb the saftey.

my cavalry arms shotgun adapter came with a rather long saftey screw and i had the same proble.  cutting down the screw instantly fixed it.