Firefox's built-in spell check can be enabled by changing the following in /lib/editor/tinymce/jscripts/tiny_mce/tiny_mce.js:
Change:
if(!v.gecko_spellcheck){q.getBody().spellcheck=0}
To:
if(!v.gecko_spellcheck){q.getBody().spellcheck=1}
You'll have to do a text search for the first line of code since tiny_mce.js is minified.
I hope this helps someone - it took me a long time to figure out.
If anyone knows of a reason why this would be bad, please post!