In this particular case, with the Logitech wireless, I wonder if part of the problem is that the Logitech mouse software has been installed?
Thanks for that tip, Milo but, yes, it is installed via the Logitech Control Center.
The consensus here is for wireless mice and I have to say I have had no trouble at all with the Apple wireless mouse. I have a sneaky feeling that the problem with my Logitech wireless mouse is that I am running it on rechargeable batteries. These start fully charged at 1.2 V whereas standard AA batteries start at 1.6 V. Just a thought.