Why might a MacBook not detect an Apple A1152 Mighty Mouse? It seemed that the USB connection was OK.  

Is there any way to solve this problem?
With a problem such as this, the first thing you must always try is to connect a different USB mouse. If one works, and the other doesn't, then the problem is almost certainly with a defective mouse, and not with the computer. This is a basic troubleshooting step known as "isolating the fault".

In all problems of this sort (not just with mice) you need to test with a second peripheral that you know is working correctly, which we refer to as the "known good" item.