Failures to fire are typically ammo or firing pin related. In 100,000s rounds, I've had less than a hand full of FTFs and they were all related to insufficient primer strikes. As TheKlawMan said, if you get a FTF, keep the gun pointed in a safe direction and wait a while before opening the action. I've never witnessed a late discharge with a shot shell, but have seen it a rifle (.375 H&H Mag) with old reloads and I was amazed by how long it took.
In my experience with factory and reloaded ammo, a blooper is a much more common problem than a true FTF. Also, with a blooper there's the potential hazard of an obstructed barrel. Years ago, a club members bought a high grade Belgian Browning O/U. The first day with the new gun, he had a blooper with factory ammo. There was enough energy for the shot to break a close incoming target, but the wad didn't clear the barrel. Since the target broke, he didn't give the light load a second thought. With his next shot, one of his barrels looked like a snake who'd swallowed an egg. If there's a shadow of a doubt, always make sure your barrel is clear.