I was surprised to see a brand new 870 today jam at the range. This guy was shooting slugs and at one point he was pumping the next round into the chamber and it got jammed underneath that spring loaded thing that you push down to load shells into the magazine (excuse my terminology). Anyway, it was jammed in there pretty tight and it took a couple of range officers to get the thing unjammed. I was a bit surpised because I've always thought that pump actions are least prone to these types of things (which is why I own an 870P). I'm not saying that I assume they're fail-proof, but it was just an observation. I should also add that the guy with the shotgun was also a shotgun-newbie so who knows what he did to get the thing jammed in there.
This is about the only "weakness" the 870 ever had, and it's been fixed by Remington.
What it is, is pure operator error.
When you load the shell into the magazine, if you fail to push it all the way in until it's caught and held by the shell releases, the shell can be pushed back out of the magazine and into the action.
On the older 870's this would cause a jam that could be hard to clear.
Some years ago, Remington started adding a "Flex-Tab" conversion to the 870. This allows you to simply pull the fore end back to open the bolt and clear the jam.
You can recognize an 870 equipped with the Flex-tab by a long "U" shaped cut in the shell lifter.
The real fix, is to just practice with the gun until you don't screw up.