New printer and apostrophes with ID documents (2.02 or 3.0)
My next guess is that you have a font conflict causing the problems, something InDesign is particularly vulnerable to.
It may be that TextEdit is picking the System X's dfont while InDesign is trying to pick another version. Best bet is to get rid of the dfonts when you have legitimate substitutes available (some programs, especially from Apple, require that certain fonts, such as Helvetica be available. They don't have to be the dfont versions, but some version must be available or the programs won't run). I got rid of the Helvetica dfonts years ago, but I always run the Adobe version of Helvetica and haven't had any problems. There are technical notes on the subject of font management under X from both Apple and Adobe, still available, I suspect, on their respective Web sites.
I'd get rid of any duplication in fonts, always preferring "regular" PostScript or OpenType fonts (or even legitimate TT fonts) over dfonts.
By the way, what version of the operating system are you running?
In addition, there is a version of Microsoft's distributed Times font (and Arial as well) that displays just such a problem when printed on a Mac. (Microsoft posted replacement fonts on its Web site a couple of years ago, and I suspect they are still there).