Spell checking in Firefox works, but you have to tell it to check. CTRL+Right-Click > Check Spelling. This will enable the built-in check-as-you-type feature of FireFox for that dialog. But you have to do this again for every message you send. Also, you need to use CTRL+Right-Click to bypass the CKeditor context menu and access the browser's context menu with the word choices.
I haven't been able to get it to work by default yet, or to work with Chrome. Not sure about other browsers.