Hi there---I inherited a pretty large jade plant a year or so ago that has recently developed some mysterious symptoms and I am worried that it is going to croak.

First off, it is dropping leaves like crazy. Many of these leaves are turning black/dark brown and look almost like they are forming tiny little crystals on them (resembling sugar crystals)??? For a while it was under attack by mealybugs, but following the suggestions found on the web, I thoroughly sprayed it down with a mixture of water with a small amount of dish soap. While this seems to have rid it of the insects, the leaf drop continues. Does anybody have any suggestions for what may ail my poor plant? I have noticed a fair amount of new growth popping up on the ends of the branches, but pretty soon it will be a naked jade tree if I keep losing mature leaves at the current rate...!

I've been having Jade plant problems myself, which has let me to a little research. That, along with some helpful people here, I've come a long way.
First off, you may be watering it too much. Mine started dropping leaves, which soon turned in to mushy stems, and what I believe to be rot. I'm not sure yet if this can be cured, but I do know that the sooner you catch it, the better chance you have.
Let the soil dry out for about a week or so, just make sure the pot has drainage so the water isn't just sitting there, which will contribute to rot. Allow the leaves to get a little wrinkly before watering again, but just be sure to keep an eye on it so it doesn't dehydrate.
Next is the amount of light. Since it's been moved, you can be almost sure that it's lighting conditions are different, and it may need some time to adjust to that. Just make sure it's getting plenty, but again keeping an eye on it as to not allow sunburn. If you can, mimic as closely as you can the conditions it was in before.
I hope this helps. I know it's pretty basic stuff, so hopefully someone else may be able to go a little more in depth. Good Luck!

~Aaron