Tony Soprano was Jersey Shore Italian. It hits the TH sound a bit softer, with the tongue a bit closer to the front towards the teeth. The Chicago accent hits that sound with a hard D, with the tongue pressing the palate further back from the teeth. Also, the S sound is harder, too, especially at the end of a word.

There's nothing wrong with his accent at all! I just wasn't used to it, and it sounded like a fake Bronx accent to me at first, until I parsed it and realized it was probably a Chicago accent.