After a LOT of trial-and-error I have these findings:
I had to completely uninstall Bluetooth Battery Monitor; this was the main culprit. Simply "exiting" wasn't enough, only when disabled on startup I was able to make some progress and only after actually uninstalling everything started working as it should. Somehow these two applications seem to interfere / bite eachother.
I had issues with the mouse "jumping", not registering any clicks (it did, until Magic Utilities was loaded), I had it showing up as "not connected" in Magic Utilities and I had it actually show up as connected whenever I unpaired and re-paired but then in less than 10 seconds it would go back to "not connected" etc. It causecaused all sorts of strange problems. Clicking / moving the mouse at times caused beeps to come out of my speaker (like in the good old days when the keyboard buffer was full or when an application hung in Win 9x.).
Uninstalling BlueTooth battery monitor fixed all my problems. Which kind of sucks since I liked it...