After reading all your replies (Thank You), and a few articles on troubleshooting residential circuits, I want to tell you about a strategy for my usual situations (partial outages on a single circuit in mobile homes), and see if you think it's ok, or if you have a better way to approach it.
Most recently, I was called to repair a circuit that had a vacuum sweeper plugged into it while the space heater was also running (most of the circuit was out). I got everything working again, but my method was a bit haphazard.
Now I'm thinking the first thing I should do when approaching this situation, is to identify all the outlets (& switched fixtures) on a given circuit, by turning its breaker off, then locating all the non-functioning outlets with 3-pronged outlet testers - I would actually buy enough of these testers so I could have one plugged into each outlet on the malfunctioning circuit, then turn it back on. Then I could start with the last working, or first non-working outlet.
After repairing the first bad one I find, I could simply eyeball the rest of the testers (in the outlets) to see what might have come back on (if any), then continue on in the same fashion as necessary 'till they're all working again. If the path of the circuit isn't obvious to me (most of the time it is - all the homes are single story), I could use a line/cable tracer to establish the first outlet in the circuit from the panel, and elsewhere when I'm not certain which direction it might take along the way.
I've found a cable tracer on Amazon.com that has all great reviews, but I'll wait for "my reviews" first on this approach to troubleshooting. Aw hell, what am I waitin' for...it's Fluke's PRO 3000 Tone & Probe Kit for about $67.00. 30 Reviews, all positive, if anyone's interested.
This product (link below) is obviously meant for network cabling, but the reviews convinced me it's good for Romex-types also. Of course, if anyone has a recommendation for one that works well and is less expensive...
Thanks so much for any help.