This appears to be an issue in TinyMCE. In 8.12 following the advice of the TinyMCE forums I've removed the spell checker as a plugin and set it to rather user the browser's own spell checking (like it does in a regular text box.) there is a complication though;
In all browsers the misspelled words are highlighted with the usual red underline. But in FF and Chrome right clicking on the word does not show the browser's suggested word list. (In IE it does.)
One alternative is to switch to Redactor which does present the word lists. I'm hopeful that a later TinyMCE release will fix this though, so I'll keep an eye out for that.
cheers
Bruce