The problem is that moxiecode (tinymce) disabled the firefox spell checker by default two or three years ago due to some bug it caused. However, no-one seems to know what the bug was, or whether it still applies. (ref: http://drupal.org/node/627180).
Open assets/plugins/tinymce/tinymce.functions.php and add this line to around line 163 (just after the existing tinymceInit lines):
$tinymceInit .= " gecko_spellcheck : \"true\",\n";
