Well after waiting around for a while, I have now installed Nvidia driver version 295.49 from the ubuntu-proposed repository. The result:
Unity 3D will run properly, but rather too slowly for my liking.
So I installed gnome-shell (Gnome 3). This runs OK with no noticeable speed problem. So I'm not sure what is causing the Unity slowness, but I have settled into using Gnome 3 quite happily.
Configuration:
64-bit Ubuntu Precise 12.04
Processor: AMD Athlon(tm) II X4 620
Graphics Processor: GeForce 6150SE nForce 430 512MB
Thanks to all who have contributed.
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