Task list as a drop down list
This is an idea attempting to solve the problem of showing minimized windows and windows requiring attention in Gnome shell.
In the top panel there is an area with the icon and the title of the active window.
If there are more windows on the current workspace, there is a small arrow on the right side of that area.
If there is a window or more of them wanting attention, a indicator is shown in the top panel area (yellow circle with exclamation on the mockup).
When mouse hovers over that area, it will expand to a drop-down list (like firefox 3 awsomebar) showing all the other windows in this workspace.
When the list is expanded, each item in the list has an icon and a window title and maybe controls on the right side so we can close or minimize windows from the list with 1 click.
Minimized windows can be presented with a certain colour or faded icon/text.
Windows requiring attention are shown with the pulsating yellow background in the list.
Alternative concept from Myxiplx
Created since the exclamation mark needs separating from the window list - in the example above, it looks like it applies to the current program. A better solution may be this:
And I propose that you can now have two lists. One as described showing all open windows (and still with those requiring attention highlighted), and a second list that only shows the windows needing attention.
Grouping / Nesting
We can also group windows in the list using a sort of a tree structure (or use it to show tabs open in an app).
While minimizing, windows are animated sliding to the task list so users know where they can find their windows.