Greg,
Interesting thread.
Your described approach is sound.
Many years ago I read this book by Roger Von Oech
http://www.amazon.com/Whack-Side-Hea.../dp/0446404667
It deals with the psychology of creative thinking and problem solving and covers these sort of approaches. If you are interested in this topic I recommend this book. The same book is also published under the title "A kick in the seat of the pants" depending which country it was released in. They are both the same book.
I have been troubleshooting complex scientific instruments (mass spectrometers) for 30 + years. These systems use combinations of chemical dosing systems, vacuum systems,pneumatic and solenoid actuators, ion optics, high voltages, magnetic fields, electronics capable of measuring one ten billionth of an amp.
There are numerous techniques I have found useful over the years :-
If something goes wrong, did I or someone else change something just before the problem arose. That's probably what caused the problem. Look at that first.
Then in no particular order : -
1. The go away and think about it method already described.
2. Also try going away and do something completely different. Forget what you did before then come back and attack the problem from a fresh viewpoint.
3.
Occam's Razor is a very powerful technique particularly in complex systems where multiple faults can cause similar symptoms.
4. Talk to someone who doesn't have expertise on that. Break the problem down into simple parts that you can explain to someone who isn't an expert. This can help clarify the problem in your own mind and let you find the root cause of the problem.
5. Talk to someone who is an expert.
6. The worst thing you can do is decide at the beginning what you think is wrong with a system based on a hunch and then go about trying to prove you are right because your ego can't take being wrong.
7. Keep an open mind particularly where the problem can be a problem caused by more than one issue compounding to create an apparently confusing symptom.
Using these techniques I have been able to diagnose systems that I am familiar with and new equipment in my labs or systems in labs other than my own that I am unfamiliar with.
Cheers
Joe Cali
...I'll fix that straight away sir 
...I do like navy blue though 
