Well, for the record, there is a spell check for User Notes, its just not the official Mac one. When editing any User Note or User Tool, just do Search menu -> Spelling (command-colon) for a spell check.
I am glad that it is there but have never used it. For many years I as a fan of SpellCatcher. I finally abandoned it when it kept creating conflicts with my updating Accordance and as Apple's internal spell checker improved. My main love for Spell Catcher was its interactive checking as one typed. I think that is the modern way of checking spelling. Waiting until one has finished typing a note and then going back and checking the spelling seems so old fashioned and inefficient.
As for Sean's point for the use of Greek, Hebrew, or other foreign words that is legitimate. But there are ways to address this since one can tell the system to "Learn words" for the most often used ones, or simply ignore the underlined words that one knows is spelled correctly. I do that all the time with proper names.
I would like to encourage the integration of the interactive spell checker into Notes (and Tools).