Turns out, according to Wikipedia, "illegitimi non carborundum" is not only one of many versions of that saying, but is also totally fallacious Latin. It is "suppozed" to mean "Don't let the bastards wear you down," but is actually nonsense.
The actual Latin for "bastard" is "nothus" and "carborundum" is a neologism based on a hard substance used for grinding (the -undum suggests a gerund, but doesn't work here). According to Henry Beard (Latin for Even More Occasions, chapter 1), the proper Latin is the following:
Noli nothis permittere te terere.
Noli is the single negative imperative (plural, nolite) and nothis is in the genitive (as they are wearing down (terendum) in relation to te, you).
Lastly, if I'm not mistaken (such a large if!), my title for this post means "Don't let errors wear you down."