When checking for continuity between two points on a PCB, how do I know it's not going through an inductor?
You can detect inductors of arbitrary size if that is the only thing on the circuit (or close to the only component). RLC or other un-lit up components (transistors) can produce unpredictable results and all bets are off as to what components are there. So I would say that this could be done on a net to detect inductance, if the assumption was that the inductor is or is not there and there were no other components (or everything on the net was high impedance and no caps).

A waveform generator and oscilloscope is usually what I've used to find values for inductors (using methods similar to the ones described here), and this could be done to find a resistor vs inductor vs capacitor. Phase changes can be detected, and even the value of the inductance obtained. 

The problem is you are probably looking for chip inductors (big ones are easy to find), and they have small inductance and resistances, which would make them hard to find. 

Another thing that I have done is used smart tweezers that can detect LRC detection. The results are limited in circuit and suffer from the same problems that ohm-ing out resistors do with other portions of the circuit in parallel.

One success that I have had in reverse engineering boards is taking a board in a dark room and shining a laser or bright light through the board to illuminate the PCB under components and see what traces are there, this works for 2-layer boards well. With 4 layer you can only see one side, so it's not as useful.