Water Heater Short...

I installed a new Whirlpool 50-Gallon Energy Smart Electric Water Heater EE2H50RD045V myself several months ago. I thought I did a good job installing it. Just my luck, after returning from a short vacation, I had no hot water. I found the circuit breaker had tripped. I noticed a burn hole in the plastic control panel of my water heater. With the power off, I removed the cover to find that one of the wire nuts melted and the wire (fortunately) shorted on the ground wire. About three inches of wire insulation melted away. I installed this unit so I figure I screwed something up. What might have happened?

Looks like you had a bad connection in the melted wirenut. The wires may have been loose, oxidized, or nicked. The wirenut may not have been been the wrong size or may have been incorrectly tightened.

Usually that means a bad connection in the wire nut, so there was added electrical resistance which caused heat and that melted the wire nut and the insulation.

Looks to me like the connection was bad.

It's hard to tell by the picture but I'm not sure that your incoming wires are the required 10 gauge wire either.
Should be all 10 gauge wired to a 30A double pole breaker.

If the factory wires to the panel are #10,which is not usually the case except for 5500 watt elements, which this unit does not have, then it appears that the customer's wires are #12. It would be even worse if the factory wires are #12, because then the connecting wires which appear to be smaller would be #14.