OK, I think I understand what it happening. It looks like Firefox is converting multiple-character unicode sequences like U+2261 U+0338 (equiv followed by combining solidus overlay) to their single-character equivalents like U+2262 (not equiv), even when the font doesn't contain the required character. The MathJax fonts don't include all the negated forms, and so MathJax uses the two-character versions in those cases. Firefox seems to recombine them, producing the missing character marker (the thin block) that you are seeing.
Personally, I consider that a Firefox bug, but perhaps I can work around it in MathJax.
Update: Here is an extension that should resolve the \not
problem in Firefox 13. Let me know if it works for you. It is a GreaseMonkey script, so you will need to install that (if you haven't already) in order to use the patch.
Update 2: Firefox 13.0.1 seems to have resolved the issue, so this extension is only needed for the initial version 13.0 and not later subversions.