Curious iTunes problem

Whenever iTunes pops up an alert to do with a connected iDevice (had two,
maybe three different ones now), and I'm in a different Space, the Dock icon
starts jumping up and down. When I switch to my iTunes Space, iTunes is
completely unresponsive and gives a dull 'bonk' sound when I try to click on
something (correctly, as there is an alert dialog waiting to be dismissed
before I can interact with the main interface again). So far, so normal.

However, the alert dialog is invisible. Well, I say invisible, but if I
activate my Space shortcut, it appears for a millisecond floating above
iTunes. Then it's gone when I go back to full-size. The only way I've found
to show it is to select 'Hide' from the iTunes Dock icon, then click the icon
again to 'show' it - then the alert is there, in front of iTunes. What on
earth is going on??

Cheers ... Mark