Is a stock Remington 870 police Magnum restricted to any kind of ammo?

As far as I know it will eat anything.  As long as it's 3" or less.

I've had a couple of shells from the cheap Walmart value packs stick in the chamber of mine, but I doubt the gun was to blame.

I also hear that they won't work with minishells.

I also had some of the Winchester 100 pack shells stick in my chamber.  The shells were for skeet/trap shooting.  Upon further inspection I found that some of the shells themselves were not perfectly cylindrical.  I had also purchased a box of the Remington 100 pack skeet/trap, they were all uniform.

My shotty is a Mossberg, but I'm sure it was the same problem.

3" and under.  

New SG's, like any gun, may need a break-in period.  It's possible that the chamber might be a little rough or the extractor has a burr, and that could result in shells hanging up.  The actual "police" 870's supposedly have a reliability job (including chamber polishing) at the factory, but who knows?

When I bought my 870P I took it to the range along with 100 rounds of Winchester skeet 2.75" shells and fired away.  It's still fairly tight compared to the old beaters at work, but it's loosening up a litle at a time.

It is illegal to use any ammo other than law enforcemnt only!