Define jam. FTF? FTE? Operator headspace and timing? (short stroking?)
The most common "jams" of 870's are (in the order of frequency I've noticed)
1. Short Stroking: Not a mechanical error, must be corrected by shooter.
2. Worn extractor, often in conjunction with worn extractor spring.
3. Worn/broken shell latches. Usually results in no feed/double feed.
4. action gunked up,can have same effects as any of the above. It takes a lot of gunk to stop an 870!
5. Although not always needed, it doesn't hurt to polish the chamber, particularly at the base. Sometimes the cheap range birdshot (Walmart 100 round paks, particularly Winchester, are notorious) have aluminum "brass" and have stuck in some guns. While some guys will say, ,"Just use good brass-based shells", it's not hard to polish the chambers so you don't have to resort to that.
6. If the guns don't have flex tabs, put them in, or mill a slot into the carrier to be able to clear prematurely released rounds. (from the shell latches)
7. Ejector. Hope it's not the ejector, they are a bit of a PITA.