Thank you for your post. I looked into this issue and found that the text area within the WebHtmlEditor is controlled by the browser and not by the control. One way to get the misspelt words to be underlined in red would be to you use the latest versions of Internet Explorer (version 10) , Google Chrome or Mozilla Firefox. If you would like to have this behavior in older versions of Internet Explorer, you can use our WebSpellChecker. The misspelt words get underlined in red in the WebSpellChecker dialog. You can find the working sample here: http://www.infragistics.com/products/aspnet/sample/html-editor/webhtmleditor-with-webspellchecker.
Do let me know if this resolves your issue. I would be glad to assist you with any further questions.
Do you require any further assistance with this matter?