General firearms safety precautions apply to shotguns and are typically included in a new gun's instruction manual. Don't worry about compatibility as long as you're using a modern gun with the right size ammo. Think about the legal problems, with the gun and ammo makers, if there were hazards. Conventional and sabot-type slugs can be safely used in rifled or smooth barrels; but, not necessarily with optimum results.
Like all guns, shooting with an obstructed barrel is to be avoided. A 20-ga shell can easily lodge itself in a 12-ga barrel. So, it's not a good idea to have 20-ga shells in your pocket when shooting 12-ga.
If your shotgun has screw-in chokes, don't shoot it without a choke in place. And, check your chokes from time to time to make sure they haven't become loose.
With pump guns, they like to be operated briskly. If you're a real slow poke stroking your pump, it may jam.
Many of the no nos have to do with best practices, and are learned with experience. Take rifles for example, certain barrel twist rates favor certain bullets; but, that doesn't mean you can't shoot any bullet. It's a lot the same with shotguns, some combinations work better than others. And, there are no hard and fast rules. It's often what works best for you in your specific gun. Look at any thread about choke selection and you'll see that there is generally a lack of consensus. Even worse, check out a thread about what's the best load for HD -- everyone has a different opinion. You'll learn by trial and error and the shared experiences of others.
CK 32, perhaps if you were to rephrase your initial question and give us an idea of what you're looking to do with a shotgun we could give you some insight more specific to your application.