What do you mean, the exe can't launch?  What happens?  Do you see an error message?  Please provide more details.

I cannot reproduce the issue.
Perhaps Chrome (you meant the browser, right? You wrote "chrom", which looks like a typo) is running as administrator?
Please see the following report:
http://tweaker.userecho.com/topic/308231-cycle-between-taskbar-buttons-stops-half-way-in-windows-8x/

So if my understanding is correct, the issue is that the tooltip is being shown for some taskbar items, but not for others. It's that right?

By default, the taskbar doesn't show tooltips when all the text is visible on the button, only when it's truncated.

Thank you for the detailed report, I could reproduce it.
Please try the latest beta version, which should fix this issue:
http://rammichael.com/7-taskbar-tweaker#download

The beta version adds support for Windows 8.1 Update 1 as well.

I don't speak German, but Google Translate gave me a rough idea about the bug.
What Windows version are you using? Does it work correctly when the tweaker is not running?

You are the first to report about this kind of issue. I can't do much with it without a way to reproduce it.
Also, why do you think it's caused by the tweaker, and not by another program?

That means that when inspector comes up, it covers the taskbar, but since the taskbar itself is redundant at that point, it doesn't matter.

Yep, that's how it worked before. I've changed it due to a request of one of the users. Overlapping the taskbar indeed seemed less correct.

Is the box only there if focus follows mouse, or did you add it for all situations?

It's there only if the "focus follows mouse" option is enabled.

Windows allows you to choose the monitor to show the clock on, by choosing which one is the main monitor.
As for displaying the clock on multiple monitors, there's an existing suggestion about it, please vote if you're interested:
http://tweaker.userecho.com/topic/378660-add-clock...

Please try the latest beta version, v4.4.6.3.