The spell checker as you describe it checks the body of the email. If you want suggestions for your misspelled word in the subject, right click the underlined entry.

Thanks, I know about right click. My point is that since the subject line is part of what I'm sending out and should be properly spelled, so an error there counts as a misspelling. And the spell checker knows this, since it puts a wavy underscore there. It's inconsistent for the spell checker to simultaneously assure me that there are no misspellings while in fact flagging a misspelling.

wavy lines come from spell check as you type. It has no user interface. So when you talk of running the spell checker you are actually running something else that does have a dialog box.

I can not find it listed as a bug however and it should be checking the subject, so perhaps you could file an appropriate bug and post a link to it here so I can set it's status to confirmed.