Martin, you've asked a very simple question that has a very complex answer. The issue of testing is such a broad subject - you can never test enough but the realities of economics and time mean that you have to limit the scope of testing. Even if your equipment passes testing does not mean that it will not fail.

In terms of your design of h/w and s/w - have another engineer check your design. Another person has a fresh look and can pick the more obvious defects. You may wish to do a search on 'FMEA (failure mode effects analysis) to start you on the path. There was also a good series of articles written by George Novacek in Circuit Cellar (issue 124,5 I think) on designing for reliability (see www.circuitcellar.com).

A good rule of thumb is that for an average design project 30% is design, 70% is testing and verification.

If you want to know more about a specific aspect of testing, first do a search on the net and expect to do a lot of reading, then ask a more concise question here. I'm sure, there are others like myself that have hard won experience and can share horror stories.