The script manager hides itself when amarok loses focus (1.4.3), and pops up again when it gains focus. This doesn't work well with focus follows mouse behaviour.

It feels like a cat and mouse game. The window dissapears just as I'm about to reach it with my mouse pointer. It takes a few attempts before I get smart enough to move the amarok window under the script manager window.

It also leads to a change in the task bar, which steals my focus; making it counter productive.

I think the best solution would be to let the script manager stay open until I close it myself.

Cannot reproduce that behavior.
I use "focus follows mousepointer", too, but the script manager stays exactly where it's supposed to be, the only way to hide it (while having it open) is to minimize Amarok, it even stays open when amarok goes to the tray.
Do you use "focus raises window automatically", too?

This isn't an Amarok issue. I think there is a setting somewhere, maybe in the Window Decoration Configuration, to change this. Sorry, I don't have Linux available right now, if you haven't figured it out by tomorrow I'll post a new post.