Fiber optic microscopes are used to inspect connectors to check the quality of the termination procedure and diagnose problems. A well made connector will have a clean, smooth, polished and scratch free finish. There is not be any signs ofcracks, chips or fiber not even with the ferrule front. The magnification for viewing connectors can be 30 to 400 power but it is best to use a medium magnification. Dealextreme sells cheap Illuminated Pocket 60X to 100X Zoom Microscope that can be used for this if you make yourself a simple adapter that hold the fiber optic connector nicely in place when you want to look at it. It is hard to keep it steady while holding it at hand. You need to work out some kind of universal adapter for 2.5mm ferrules (works with FC/SC/ST connectors) and maybe another for 1.25 mm ferrules (LC and MU connectors) to keep the fiber well in place when you look at it.
A lot of “bad” fibers can be traced back to dirty connectors. You can see the dirt with microscope. But usually it is always easiest just to clean the connector every time you suspect it could be dirty. So always clean the fiber before plugging it into an interface. Cisco document Inspection and Cleaning Procedures for Fiber-Optic Connections gives you a lot of information on fiber connector cleaning.
WARNING: Remember to check that no power is present in the cable before you look at it in a microscope to protect your eyes! The microscope will concentrate any power in the fiber and focus it into your eye with potentially hazardous results. Some commercial fiver microscopes have laser safety filter in them but this DIY model does not have it.