As for Shotguns the worst I've ever owned was by far a Remington 870 Express Super Magnum. The gun just had one problem after another. Right out of the box it wouldn't cycle 2 3/4" shells. The pump would stick every few shots and you'd have a heck of a time getting it open. Then with 3" and 3.5" shells it also jammed way more often than it should, only it didn't have the pump stick, it just had random type jams. Sometimes it would stovepipe, several times it would try to feed 2 shells at once, sometimes it wouldn't pull the fired shell out of the chamber and would try to chamber another one. All in all, it probably jammed at least 1 or 2 times out of every 20 times and that's on the low side with Buckshot, and it jammed about 1 or 2 times out of every 5 with 2 3/4" shells. I missed several deer due to jams with it. That's what finally made me get fed up with it.
I also had a gunsmith polish the chamber, and it did fix the issue with 2 3/4" shells sticking, but it still had the random jams fairly often., Way too often for my liking. Not to mention it was cheap horribly finished wood, and a cheap finish on the rest of the gun. The thing didn't patter near as tight as I'd like. I just really don't have anything positive I can say about the 870 express models. For the $350 it costs, it was horrible, as while $350 isn't a ton, it's not cheap either, and should buy you a gun that works.
As for rifles, I've never really had a bad rifle. Everyone of the ones I've had has been pretty good. I did have a Browning BAR 30-06 that wasn't very accurate and shot 3-6" groups with most all of the ammo I tried. I finally found Federal Fusions and it reduced my group size to 2" or so at 100 yards. It's the only ammo I found that would shoot under a 3" group in this thing including the handloads I tried, but it seems to do well with that ammo so I just stuck with it. This wasn't my favorite rifle because of the lack of accuracy, but it still was a good rifle, as it was very reliable and plenty accurate for a deer rifle which is what it was intended to be.