ALL guns have problems.
The 870 is certainly the toughest, most durable, and trouble-free pump gun of modern times.
It's because the 870 is so trouble-free that the police use it almost to the exclusion of all other shotguns.
Make no mistake, the Remington 870 is a TANK.
The only "weakness" the 870 has is strictly user induced.
This is a situation where when loading the magazine, a shell isn't pushed ALL the way into the magazine, and it slips back out, and back into the receiver.
With older 870's, the shell would jam the action, since with the bolt closed, you couldn't open the action to clear the jam, and had to remove the trigger group to clear it.
Newer 870's have a "Flex-Tab" conversion that allows a mis-fed round to be cleared by simply forcibly pulling the action open.
Flex-Tab equipped guns can be recognized by a rectangular, "U" shaped cut in the bottom of the shell lifter.
All 870's made in at least the last 10 years or so have it.
Since this type of jam is "operator error", the "fix" is to train with the gun to eliminate any chance of fumbling a reload.
In truth, with newer 870's with the Flex-Tab, this is largely a non-issue.
As to keeping a round in the chamber......why?
The best way to carry or store a pump gun in a ready condition is in the police "cruiser ready" condition.
To do this, check the gun over to be sure every things in good shape, close the slide and (pointing in a safe direction) pull the trigger.
Then, load the magazine and it's safe to carry or store.
The gun is 100% safe in this condition, and all that's needed to use it, is to pump the action to chamber a round.
If you need to keep a round in the chamber for some legit reason, remember that this is NOT a very safe method for ANY shotgun, due to the fact that the safety only blocks the trigger.
Treat a fully loaded pump gun like a live hand grenade.
Unless you do have good reason to keep the chamber loaded, use the Cruiser ready method. It's MUCH easier and there's less risk of fumbling around trying to "find" a small safety button, when all you have to do is grab a large handle and pump it.