Which OS version are you specifically referring to?
The spelling and grammar checks have changed over the releases.
I just checked on 10.4.11, and it doesn't consider "ohio" to be misspelled. It also has no ability to put initial caps on sentences. At most, it will match the capitalization of the text that it finds.
On 10.8.4, the spelling check seems both stupider and smarter. For example, it won't suggest USING for USNG because it thinks USNG may be an initialism. This would be stupid IF I'M USNG ALL-CAPS, but smart if I'm referring to the
USNG.
In order to see corrections for initial caps or uncapped i, you have to turn on "check grammar".
To do this, press command-: (Edit > Spelling and Grammar > Show Spelling and Grammar), then check the checkbox for "check grammar". This is for 10.8.4; what you see may vary if your OS version differs. I don't recall if there's a global setting for this in a System Preferences pane or not.
FWIW, its recognition of state names seems quirky. "Check grammar" must be turned on to recognize an uncapped "ohio", but an uncapped "arkansas" is always recognized. Maybe "ohio" is a valid non-proper noun in some contexts; I don't know, that's just a guess.