I believe there ought to be a graphical indicator of new/modified/saved status for the currently open file, rather than the "character mode era" trend of appending an asterisk to the end of a filename.
An indicator "light" graphic could signify document status (saved, modified, new) by color. This icon could appear in the lower status area of the main window, or within the tabs themselves. One of the best editors I've ever used (for PL/SQL programming) used two thin LED-style colored glyphs as the 'icon' on each tab. The color state of the glyphs gave you a bird's eye view of what you've modified, what has been opened but not touched, and what you have recently modified within this session. It was very easy to become acquainted with the colors.
Colors are better from a usability standpoint than appending a character to the filename display. You can read them from the corners of your eyes, rather than having to focus on each text element and check for an asterisk.