NorwoodG, thanks for your reply!
I have used the same display since 2006 with a Quad G5, with no problems. The stripes appeared first time when I connected the display to my MacBook Pro. Maybe the display is incompatible with some Intel Macs, dunno... If you have the same problem without using the Mini Displayport to Dual-link DVI adapter, that kind of makes clear that the issue is not related to the adapter.
It would be nice to try if the problem appears with newer 30" Cinemas, but not so many Apple resellers have them unboxed in store to try out here in Finland... Have you had the opportunity to try out an another 30" Cinema?