It is sometimes hard to be sure if a variable inductor is bad or not. You can test to see if it is open or shorted, and it is very difficult to test for a core to coil short without special equipment and good specs, but in my experience with radios, the most common problem with them is the core is cracked/broken due to people using metal or ceramic screwdrivers to adjust them. The ferrite core is very brittle, and will crack very easily, and sometimes it will be difficult to tell without removing the core.
If you suspect the inductor to be bad, disconnect one of the leads and check for continuity, and a fairly small resistance, such as 2-3 ohms. No continuity is a bad inductor. If you have continuity, it is most likely something wrong with the core. If you can still turn the core, turn it until it comes out, and see if there is a crack in the core. If you pull it out, and the core is cracked, you can sometimes pull the core out, remove the broken portion, and insert it in backwards and it will still work to get the output you want. If you can't turn the core from the top, you have to remove the inductor and screw it out from the bottom.
If removing the broken portion and reinserting the core upside down doesn't work, you will likely have to replace the inductor, unless you have spare cores, which is unlikely unless you work on radios and remove the cores from the parts chassis you have.
Anyway, there is more to it than that, but that would cover 95% of all inductor faults.