OK, so it's not fully automatic, but as a terrible speller here's what I do to make certain that everything is correct within my Revit sets.

As you know, the spell checker in Revit only spell checks the text within that open view, not the whole project, and not text within a schedule, keynote, sheet name, or view title. This is great for notes and details and such, but not so good for keynotes and comments on the door schedules. You could cut 'n paste those item's text into a note in a view and then spell check that, but I've got something a lot faster.

If you don't have one, generate a schedule of your view titles / sheet names / door comments / keynotes / whatever it is you want to spell check or open your existing schedule. Then go to File -> Export -> Schedule on the menu, and export a .txt file of your schedule. Open that file in Excel or OpenOffice, and hit F7 to spell check it. Now you'll see where all your misspellings and typos are, and you can then go back into Revit and pick them up. I tend to just cut 'n paste the text from Excel into Revit, but that's me. If you were worried about misspellings project wide, export instead to Excel/OpenOffice via ODBC and then you can check the whole project at once...

Like I said, it's not automatic, but it's better than nothing and a big help to me, a horrible speller. Hope it helps you out too!