I've learned that GOG's version of the game is apparently the "Digital Jesters" version of the game, which is, so I've heard, inferior to other versions. What, exactly, is wrong with it? And is it possible to fix those problems?

I have had no problems with GoG's version on XP - Except for the occasional crash to desk top which only happens very rarely Compatibility mode for other OS's does not help. I consider this issue to be minor and rare. This is where the Save Game feature comes in handy. The price you pay for this great game and the entertainment value far exceeds any minor problem. Long Live Freedom Force and GoG!

If this is true, then it is a bad, bad thing.
Digital Jesters severely altered their version of the game before releasing it. Basically, they altered the file structure which makes modding nearly impossible. The game itself should run just fine, but you're stuck with the base game mostly. And forget trying to mod it yourself.
I'd rather wait for confirmation, but if this is true, then avoid this version of the game like the plague, unless you really don't care for modding or installing new characters and such.
EDIT: I bought it and checked it out, and I'm happy to say that this is NOT the DJ version. It should be fully compatible with all mods, skins, and meshes, although you will have to change the shortcut directory for mods.

I am filled with happiness, as I purchased this game primarily for its extensive moddability. I looked at the Freedom Reborn forums; the "FFvTTR coming to GOG!" thread, where Epimethee said that it was the DJ version, so that's why I thought it was.
Thanks for your help!

I have already confirmed the ability to add meshes and skins. For more information, see the post: GUIDE On Installing Meshes And Skins.

Verrrry happy to learn that my fears were not justified. :)