With changeset 8918 I've updated OpenNI to the newest unstable version (126.96.36.199). All the changes are internal to Candescent NUI and don't influence it's public interface.
I've also updated to the newest driver Avin2 SensorKinect. There you can find instructions on the installation order (OpenNI, then the driver, then NITE).
I've installed the 32-bit version on my 64-bit Windows PC without problems (this time).