Tonight my 1981 Case 580D Backhoe started shooting sparks from out of the muffler. Does anyone know what this means? I had to shut it off so I didn't start a fire.

gosh fred, this could mean alot of things, from minor to major.
Minor= internal muffler components burning and being expelled. ie, fiberglass, spark arrestor screen. Carbon buildup would look like red hot embers, if it were being expelled.
Major= bits of internal combustion chamber parts. ie, piston, rings, (spark plugs, ha), glow plug, etc.

We used to pour water through the intake on a gasoline engine while it was running at a fast idle. the steam created would crystalize the carbon and clean it off of the valves and pistons. We did this to eliminate "dieseling".

If its not too much of a problem, remove the muffler, turn it upside down, tap it onto the concrete. check what comes out. And while the muffler is off, start it up and run it and see if you still get embers.....sl