Mac: Software using AXUIElementCopyElementAtPosition make all Qt programs crash

In Qt Creator the following actions result in a crash:

• attempt to drag the window using the title bar
• click anywhere on the left sidebar

Thankfully, the shortcuts for switching to edit/debug/... view still worked.

Yes, I'm aware that this sounds incredible, but it is happening. Even after removing all Qt Creator settings (I upgraded from some 0.9 alpha or beta or final straight to 1.3.0), the same behavior is reproducible.
I've collected a whole bunch of stack traces. I hope they can help you pinpoint the problem.