I created a question with \varnothing to denote empty set.
In the preview it played nice, but on the question page \varnothing was replaced with \emptyset for some mysterious reason.
Why \varnothing does not work?
Well, it seems to work for me. That's too bad.
MathJax v2.1 should resolve this issue. Math.SE is now using the beta version of MathJax v2.1, so you should see the correct rendering for these characters now (both the empty sets and the setminus issues should be fixed). Please let me know if that is not the case.
Note that if you keep your browser open continually, you may need to empty the cache and reload the page (or perhaps even restart the browser) to get the new copy of MathJax. (MathJax's About box should tell you which version you are getting; make sure all the files in the list show v2.1).
See MathJax 2.1 beta for more details on the changes in MathJax v2.1.