The bad tube thread was pretty interesting and got me thinking about a transistor thread. So I was wondering how you experts determine bad transistors while they're in circuits, are there any tricks to use multimeters to find issues?
It's hard to do a quantitative test (i.e. "gain = 124, leakage = 106nA) in circuit. But you can do some qualitative tests. That is in fact, part of the basis of "What to do when it doesn't work". I suggest you read "What to do when it doesn't work" with an eye to what it tells you about operating voltages, and think about why this is such a remarkably useful set of tests. I don't even count any more the number of times we've debugged a bum effect by simply looking at the voltages from this test. It's not perfect, by any means, but it's really, really good for sorting out the "nothing works" cases.
In a small signal NPN working as an amplifier and not as an on-off switch, the emitter will always be 0.4 to 0.7V below the base, and the collector will be at a higher voltage than the base. When the collector gets lower than the base, the device is saturated and can't be amplifying. How much above the base the collector stays is dependent on the circuit, but the Collector -> Base -> Emitter voltage cascade must be true, or it's not amplifying.
If the base and emitter voltages are the same, the device may be internally or externally (i.e. bad soldering) shorted base to emitter, or the base may be open, no drive applied. If the collector and emitter are the same voltage, either the collector load is open, or the device is internally or externally shorted.
The same is true of PNPs, but in the opposite direction: Ve > Vb by 0.4 to 0.7V, Vb > Vc by some amount. For both NPN and PNP, the "some amount" the collector is away from the base is most often a significant fraction of the power supply, 1/3 or more. There exist special cases where this is not true, but mostly.
Sometimes the resistors on the base are so large that you can't directly measure Vb and Ve then subtract and get sane measurements. In that case, measure with one probe on the base and one on the emitter directly to get Vbe.