Generally the only problems I'm aware of relate to sending things down the drain that shouldn't be (e.g. excess cleaners that can kill off the bacteria, lots of grease/oils that may clog the drain field lines),and too much or even too little waste going to the system. ...or the drain field being damaged/compromised in some way (usually trees taking root).....
Fundamentally a septic system relies on bacteria to break solid wastes down, and the drain field releases the liquids (and water-borne solids) to be filtered through the ground releasing the water back into the environment. ....so really the problems tend to be killing/starving the bacteria, or clogging the system. ..... generally not too much of a maintenance hassle, but I'm no pro either.