Have the same issue in Aperture 3.4.5. Aperture will present the spinning beach ball until Mac OS X pops up a message about running out of application memory on my startup disk.
I have tried all options of rebuilding the Aperture library (permissions, etc.) and also have tried importing all photos into a new Aperture library. (All this as per recommendation from an Aperture expert at a Genius Bar).
Still dealing with exactly the same problem.
Will now try to reinstall Aperture.