Performance should not be an issue if the check is not done from filter. IMO there could be some spellchecking-formatting function in weblib.php (similar to highlight). Each module would call it when appropriate. Example: forum posts would be checked only as long as editable. There could be also some icon (for teacher only) to force spell checking of resources.
Another solution could be to make it as true filter and place some special tags into those new Smarty templates. Filter would know exactly what to check - to save work and to prevent students from checking teachers posts
Thinking about the spell checking engine, we could store aspell's dictionary in database and do the checks by sql selects - maybe it would be even faster ?? It would also be platform independent, we could store user dictionaries in database too (aspell's user dictionaries would be extremely problematic).
BTW the code above is pretty lame, I do not recommend installing it