skins/common/commonElements.css currently contains a rather obtrusive style rule that messes up font rendering:
font-family: Times, "Times New Roman", serif;
This is very old code that has been present long before <q> was allowed in wikitext. I suspect that it was added because IE <= 7 doesn't insert quotation marks around <q>, as it should. So the rule was put in to make quotes at least somehow recognizable.
I don't think this is still justified (IE >= 8 and all other browsers insert quotation marks properly). The rule should be dropped or at least a CSS hack should be used to hide it from modern browsers.