I loaded Wrye Mash today after editing a skill speed in Wakeem's Game Improvements in order to restore the load date I had set. When I started Wrye, it said this:

The following save files have corrupted headers: Restore.ess

I have no save game by that name so I don't know what this means or how to fix it. What do I do?

I don't know how to hep you, but Restore.ess is sometimes auto generated when the game crashes, not to desktop but like crashes within the game.

Does that mean I can move the file (if I can even find it) and let it remake itself?

You could try it, it wont matter hurt if you delete it. If it was ever generated it should be in C:\Program Files (x86)\Bethesda Softworks\Morrowind\Saves or if you are using a 32bit system then: C:\Program Files\Bethesda Softworks\Morrowind\Saves

I located the file by opening the "Saves" folder, along with another one called Restore.tes. Wrye Mash doesn't show them at all, but for some reason reports errors in the one mentioned anyway. Is the tes version just a newer copy? What do they actually do that would necessitate the game keeping them around?

I never seen the .tes its not a save file. Could possibly be how the game creates the .ess on a crash. There really shouldn't be anything that you would really need them for, if you quick save enough (as you should) restore.ess wouldn't make much of a difference anyways. Try deleting that the problematic one and ignore the .tes unless it also causing a problem.

The file extension ".tes" is how Morrowind creates temporary names for save games while it is writing them. When it is done, it renames the ".tes" file to ".ess". If Morrowind should crash during this process, the .tes files will remain. It may be a partial or complete save game, you won't know unless you look at it with a savegame editor. Probably best to just get rid of it.

Gotcha, that helps a lot. I have had a couple of the more "hard core" crashes on this installation and that probably explains at least the corrupted file. All my real saves seem to be peachy though.