@ Rainy-Day: Thanks for being detailed, it helps a lot to duplicate problems (I can't fix them if I can't duplicate them usually

).
1) EDIT: I actually just spotted a few lines to comment out which have mostly fixed what I wrote about below:
I see what you mean now. This is a combination of what I was describing and the fact that I deliberately prevented docked windows from being minimised (with a timer) when they don't have focus (at the time I felt that a minimised docked window could be kind of confusing to try and find). I can fix the first aspect of the problem and probably will allow docked windows to be minimised in future as I think I improved the code since last time and unminimising should show the docked window because it would have keyboard focus, although it would almost certainly lose it again because of the mouse not being over it. Which leads me to another thought, maybe I can count the window as "having the mouse over it" if the taskbar has focus - that way it won't flash too quickly even if it does hide again. Oh and I did originally have it so that when hiding a docked window, the focus would go to whatever is under the mouse, but this has issues - such as having to be careful where you put the mouse unless you have a maximised window behind the docked window (it got pretty annoying to have the focus jump around "accidentally" with lots of windows open on the screen, wheras this way it is more or less the same as alt-tab switching).
2) Yes I can reproduce this one. The code for hiding the docked window (re-docking) should be checking that the focused window has the same PID to avoid just this sort of problem - I'll have to see what's up with it
3) It's happened to me too a few times, but not in quite some time except when trying to alt-tab before the script has had a chance to run fully when starting it. I believe it could be a sort of bug in the AHK hotkeys code when under some circumstances it doesn't catch the key presses (not sure what circumstances though). If you manage to figure out a way to reproduce it I can try and reproduce the bug and report the error to Chris or something (the hotkeys for alt+tab or turned on at the start of the script and don't get turned off again any time, only the extra ones such as alt+wheelup/down and alt-esc). It might also be worth mentioning to Chris if it's happening to you often - like I said, it's not happened to me for some time so it's not a bug I'm concerned about (and I alt-tab quite a lot... well you'd sort of expect the nature of my script

).
4) I use the classic windows theme so don't have round borders. Can you check it is this that's causing the problem by trying it out with notepad - otherwise it sounds like a program-specific issue.