It appears that there is no way to get Word to spell check the smart art, nor will it check the words that appear in other graphic formats.

In the case of Smart art, you 'can' copy the text from the dialog where you edit it and paste it into the body of the document to spell check it there. Certainly not a great way to work but it does provide a pathway to spell check your smart art content

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Andrew Lockton
Chrysalis Design, Melbourne Australia