Moodle no longer uses its own spell checker in a text edit window -- like when you post to a forum. Instead, use the spell checker that is built into every current browser (Firefox, Chrome, Internet Explorer, Safari).
Simply CTRL+Right Click (Windows) or CTRL+Click (Mac) on a misspelled word (shows as underlined in red), and the browser's built in spell checker will be activated. Please contact the Help Desk if you have any questions.