1. Open a schematic. Move a part. Then undo the move with ^Z. The modified "*" on the tab stays on.
2. Click "Save". You get the "Nothing changed" dialog box, but the modified "*" still stays on.
3. And you can't close the tab without getting the "Your file hasn't been saved. Would you like to save it now?" dialog. Clicking "Close" does indeed close the modified-but-not-really-modified schematic. But the modified "*" should either go away if there aren't really any changes (like Undo rolls back to the state when the last Save took place), or if you hit "Save" and get "Nothing changed".