Turbo Tax has entered the wrong state (IL) for the Department of the Treasury. It should be MN. It flags the accurate zip code as an error. How can I fix it?

You have to exit the review to fix that error.   Search for 1099-INT and use the Jump to link.   From the summary, edit the form that needs the state updated.   Then you can go back to the review and finish filing.  

Check the 2-letter state code for that zip code.   Make sure the city and state match up to the zip code.  This error happens when the state code doesn't match what is on file with the IRS.  TurboTax follows the IRS for acceptable zip codes.  If the state code does not match the correct state, you will get an e-filing error.   Correcting the state code is usually the fix.  

• Check that the 2 letter state abbreviation is correct here USPS Two–Letter State and Possession Abbreviations   (most common error)
• Make sure you've entered the ZIP code in either 5-digit or 9-digit format, for example, 12345 or 12345-6789.
• Look up the correct ZIP code for the street address in question.