What are the most common causes for hysteresis in the rear derailler?
Here is the list of things I usually check for when troubleshooting jumping gears:


Is the chain always goes up/down? In this case usually the adjustment is off. Try adjust the cable.
Is the mech hanger bent? Sometimes during a crash you can bend a mech hanger. Most of the times you can bend it back, but there are cases where you need to replace the mech hanger for a new one. Usually they are cheap £5-15. 
Is the shifting very slow? Dirty outer cables and rusty inner can cause the problem with shifting. Replace inner cable and outer cable for new ones.
Is the shifter clicking OK? I've seen cheap shifter wearing out and not "holding" clicks properly, so the chain would jump.
Are the mech cogs (small chainrings) worn out? are they wobbly? Chain can only be placed properly if the cog is not moving sideways. If that is the case, replace the top cog. Also worn out cog can affect the shifting performance.
Is the mech itself not bent or otherwise damaged? There are plenty of ways to destroy the mech.. usually that is beyond repair and you need to get a new one.
If the mech is very-very cheap, it sometimes gets bent while in normal use (not MTB abuse). Only replacement will fix that.


Good luck! And I'm off to fix my wife's bike gears -)