First, a few definitions:
A shell (or any device for that matter) that leaves the mortar, but fails to function in the air coming back down unexploded.
A misfire occurs when fire has been presented to a device, and the device failed to function entirely, not ever leaving the tube. Now keep in mind, if you hit a cue, and the electric match is bad and does not function, that in legal terms, is not a misfire since fire was never presented to the device.
A hangfire occurs when fire has been presented to a device, the device failed to function during the show but continues to smolder, and fires at some point after the show. Hangfires are very dangerous, as it is not always apparent that a device is still live in the gun at the end of a show. Hangfires have been known to happen even 30 minutes after a display has finished. Because of this, it is imperative that the crew stays clear of all the guns, until the operator in charge has finished his inspection and gives an "all clear."
Ah! A DUD!
What does a fireworks dud look like?
Depending on the size, a dud will look like a burnt tennis ball, softball, or larger. The larger shells usually appear slightly deformed due to their greater momentum upon impact with the ground. For this same reason they can be split wide open in some cases. But either way it should resemble a burnt, somewhat spherical object. The picture above is of a 4" dud soaking in a bucket of water. The two things you see poking out of the dud are the time fuses. Some shells have one, some have two. Most of the larger shells will have two to ensure ignition, but from the picture we can see that that is not 100% fool proof.
So what do I do with the dud?
The law (California) states you must pick up the dud with a shovel, and immediately place it in a bucket of waiting water. As an additional safety measure, you should mark it's location, and keep everyone away from it for at least 20 minutes. Pick up the dud when you are done striking your show to give it ample time to cool.