Firefox tabs have a spinning throbber letting you know they're working. It would be handy to have this feature on gnome-terminal tabs. If a shell's process has returned to the command prompt, there'd be either no throbber or an icon indicating its ready for input. If the shell is not at a prompt, the throbber/icon would be in a state indicating that its working.

Ideally, the throbber would indicate if stdin was available. This way, you could have an animated throbber meaning "working." However, that may be quite difficult... in that case, if its only easy to detect if the process has returned, it would not be good to animate the throbber... it would be way too annoying using vim or emacs and have the throbber constantly turning.

As an alternative, maybe the font on the tab or the tab background color could indicate a change in status.

This is most useful if you are in one tab working waiting for a process in another tab to finish, or if you are in a different program waiting for a process to finish.

Maybe a more sophisticated system could work like xchat-gnome... if the tab or gnome-terminal is not focused, and its state changes, it would indicate so visually. However, if the tab is active then no visual indication will be shown.