I see Woody "beat me to it", I was typing while he was posting
The problem with mounting a scope on the receiver of any of the take down pumps like the 870, BPS, Ithaca....etc. is that there is always some "play" between the barrel and the receiver.
The barrels on these guns can move around a bit in relationship to the receiver. This is not a problem or noticeable when shooting a shot patern at a duck or trap target at 35 to 40 yards but it is an issue firing slugs when the scope is on the receiver, not the barrel.
Attaching a scope base to the receiver will cut down on the potential movement between a saddle mount and the receiver nut there still will be movement between the barrel and the receiver.
Ithaca has got around this on one of the latest "Deerslayers" by perminantly mounting the barrel to the receiver like a rifle. The 37 can get away with this because the bolt comes out the back of the receiver for dissassembly (with the butt stock off the gun).
http://www.ithacagun.com/product/firear ... erII.shtml
The description mentions this feature. However, this Ithaca model is very specialized and limited in what it can be used for.
I am afraid it I wanted to scope an 870 for slug for my own use, I would buy the cantalever deer barrel.
I base this on 35+ years of shotgun experience. I used Ithacas a lot from 1970 to about 1978. I have hunted with 870's since 1972 and the trap versions have been my "main" trap gun since 1976, even though I have more costly o/u's. I have been to the Remington Shooting School and the factory at Ilion NY and have discussed this issue there. These are a few of the things I base my comments on.