If by the 'normal' spell checker you mean the one built into OS X, you can use it in the regular (non-html) editor modes. First, make sure it is turned on in the browser app's Edit menu > Spelling and Grammar > "Check Spelling While Typing" menu item. That will underline potential misspellings in red, just like for other apps that support system-wide text services.
It's not working for me. I have the spell checker turned on in TenFourFox 4.0.1. This is a ported version of Firefox 4.x. Interesting enough I got spell checking turned on by control click > check spelling. I see that check spelling is now checked in the control click box.Now, I have html & TenFourFox underlined in red dots.
Do you get the underlining to work in other browser without this maneuver?
The trick is you can't access the OS X popup contextual menu with a right click on the underlined word because that brings up the ASC insert/align menu. But you can do it with a control click. This is because of a quirk of the software running the site, which is neither developed by Apple nor platform specific.
There is a way of injecting javascript into a page. I bet you could zap away the forum right click via the injected javascript.
Robert