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.

(Maybe I should try installing an older version to see if I can confirm what I am claiming, but I don't know where to find older versions, since installing the new one clobbered the old one.)

Yes, this is interesting. You can grab old versions of the tweaker here:
https://www.dropbox.com/sh/mcbychsh0xc1dvu/8-Lj2sg...

The trouble with checking for the focus-follows-mouse setting is that if MS changes how they store that, the fix will no longer work, but if you want to do it that way, I have no problem with that.

This is documented, and shouldn't change in the future.
SPI_GETACTIVEWINDOWTRACKING

Also, I assume you mean click on desktop, not on a blank area of inspector. The latter would be bad, imho, since clicking on something usually selects it, not closes it.

Actually, I meant the inspector window, not the desktop. And that's why I talked about the right click.

As yet another option, what you might want to do is add yet another checkbox to the tweaker menu to toggle exit by focus vs exit by click.

I don't think there's a need for an option - detecting the accessibility option should work. The question is - what kind of click should trigger exiting?

And, yet another option is instead of checking whether focus follows mouse is set, you might instead want to check the menu delay

I'm not sure that it's related, and even if it is, I prefer not to change it with the tweaker.

Anyway, you're probably the only tweaker user who has this accessibility feature turned on, so think about a preferred exiting method (which is not difficult to implement :)) that you'd like to have.