Is there a simple way to compare versions of show files between saves? Or what has changed recently to cause the asterisk to appear?

No, there isn't. Command History (Tab 30) or the log files will have some clues to what happened.

I just tried a quick search of the Manual to see if Command History (Tab 30) persists between console restarts and it appears that it does not?

"Command histories are kept for each editing session, which begins when a new show file is created or when an existing show file is opened, merged, or imported."

As mentioned in the Facebook group today, sometimes I see the asterisk when I start the board and I'm not sure what has changed, who changed it, and if I want to save that change.  (I'm not the only one who uses the board...).

To look at Logs I'd have to leave the EOS program, go to Settings, Maintenance, Save Logs, and then open the resulting file?

I just tried a quick search of the Manual to see if Command History (Tab 30) persists between console restarts and it appears that it does not?

"Command histories are kept for each editing session, which begins when a new show file is created or when an existing show file is opened, merged, or imported."

As mentioned in the Facebook group today, sometimes I see the asterisk when I start the board and I'm not sure what has changed, who changed it, and if I want to save that change.  (I'm not the only one who uses the board...).

To look at Logs I'd have to leave the EOS program, go to Settings, Maintenance, Save Logs, and then open the resulting file?