I Have An 870 I Picked Up From A Good Friend But Ive Never Had Any Problems With Mine But I Would Take It To YOur Local Gun Smith And See What He Says
Happy Shooting,
Chance Pendergrass
All four of my 870's have the same bbl. play described by Chance. Quite noticeable in my older two guns. Not as much in my two newer Scattergun Techs. All caps are finger tight only.
Remove the cap, and the bbl.s come off slick as a whistle. Just like they're supposed to. Even with the bolt locked forward.
I might borrow a new bbl. just to see if that tightens things up a bit. If not, it's the receiver fit, or combination of both bbl. and receiver.
NOTE: Side to side play is OK to a reasonable degree. Don't think yours is unreasonable. However, back and forth play is not normal when the cap is finger snug.