I apologize for my ignorance on the subject and I ask you to reassign this bug
It seems that whatever algorithm the "fonts' subsystem" is using to select the
fonts it will export as 'serif', 'sans-serif' etc., it is making bad choices
for non-latin scripts.
1) Open up icedove and try to compose a message in Greek. Icedove will report
the font as 'sans-serif' and the text will look nice.
2) Install package ttf-bitstream-vera.
3) Repeat step one. Now some fonts (noticeably the small greek letter pi) will
look quite ugly. It seems a math font is being used, which does not look
acceptably good in normal text.
4) Removing ttf-bitstream-vera fixes the problem.
Installing a new font on your system should not break installed apps, hence I
am reporting this as a bug. In particular Bitstream Vera (as fas as I know)
does not contain a Greek script (expept perhaps the troublesome letter pi), and
hence is not suitable as a default global 'sans-serif' font. Alternatively, the
fallback Greek script should be selected (as a whole) out of a font which
supports the whole range of Greek characters.