Works as expected for me. Please provide a way to reproduce the issue.

From what I understand, it's a duplicate of:
http://tweaker.userecho.com/topic/178787-group-id-...

Please see my reply there.

Closing as a duplicate of:
http://tweaker.userecho.com/topic/382920-after-wak...

You're using Windows 7, right?
All the crash reports specify Windows 7. I'm not sure what causes the issue, except that it's something in the update checker, but seems like it's a Windows-7-only issue.

When I left-click on the Taskbar

Do you mean double left-click?

it displays the Alt+Tab menu window

Do you mean the Ctrl+Alt+Tab option?

It would be much more productive if, immediately after launching it, the Alt+Tab clicking could be replaced by wheel scrolling on my mouse, as long as it stayed hovered over the Taskbar.

Doesn't it work this way already?

Please try the latest beta version, 4.5.1.2.

OK, I could reproduce it. Seems like it only happens on Windows 7. I'll see what I can do.

OK, I understand what you mean.
That happens because when you're using an option of the tweaker (such as minimize to scroll), the tweaker does the minimization, so it can control the behavior. When you click on a taskbar button, explorer does it, so the nocheck_minimize option has no effect

Closed due to a lack of feedback. Please leave a reply if there's new information.

Works for me, tested on the run dialog (Win+R).
Perhaps you've encountered it with a window which uses custom thumbnails as tabs (e.g. like IE does), and then the minimizing mechanism is different, and there's no way to force it to minimize.

I can't reproduce it. The group stays expanded until you move the mouse out of the group on my PC.
Please provide more details, such as OS version, taskbar properties, and tweaker options.