Is there an automatic spellcheck module for the HTML editor, such as automatically underlining the misspelled word as one types?
There is Benjamin. You can you the editor's ABC on each of the editors on Moodle. You can try it here, too. You can also enable your computer and/or browser to do the spell check automatically and then it works anywhere you write. Here's more on that: http://support.google.com/toolbar/bin/answer.py?hl=en&answer=32703