(What an appalling interface Gmail is...) anyway, a quick test shows that you can check your spellings (using the Gmail interface but not the in-built OS X system) and get corrections suggested, but only if your message is in plain text format:
However, if it is in rich text format (which appears to be the default), incorrectly spelt words are highlighted, but no suggested corrections are presented when you click the word:
The equivalent version of WebKit that OmniWeb is using also suffers the same problem. The current release of Safari only supports plain text entry and therefore works for spelling checks (though the OS X service is also supported for some reason whereas it isn't in later versions of WebKit). Therefore, since the version that Safari is currently based on, something has changed in WebKit that enables it to support rich text entry, but not the spelling feature of Gmail.
The solution, therefore, is to convert to plain text entry if you wish to continue using OmniWeb. Personally, I would avoid using a browser altogether and set up Mail as your Gmail client, but that is me ;)