More suggestions Rated 5 out of 5 stars
Another vote for: Click on the group in the menu to select the last selected tab in that group.
Also, another interesting idea:
Have an option to make each group its own dropdown menu. The title of the menu would be the group's name (or possibly an icon, selected from a preset list).
[Social sites v] [Music v] [Games v]
These menus could live on the right side of the tab bar, to the left of the groups area.
This feature would be optional - the current solution is also good. This would allow you to select tabs with 2 clicks instead of 3.
"Click on the group in the menu to select the last selected tab in that group."
I have uploaded a test version with that feature
0.4.1 => https://addons.mozilla.org/en-US/firefox/addon/tabgroups-menu/versions/