A potmeter is a variable resistor... so measure ohms instead of continuity
i'll try to explane as far as i know it,
Experts here, please correct me if i am wrong, so i learn also

I made a sketch of the inside of a potmeter in 4 situations:

As you may know, the path that electricity likes is the one of less resistance..
so lets say this is a 100K ohm potmeter, the red line represents the resistance in the potmeter, the blue with the arrow represents the contact that is variable.
I drew the green line as an example path if you enter the potmeter at terminal "A" of the potmeter and terminal "B" as the "exit"
Lets say in an optimal situation that the resistance in example "1" is 0 Ohm, since that is the shortest path.
in example 3 the resistence should be 100K ohms, as for example 2, it should be a around 55 -60 K Ohm
In theory if the potmeter is broken (example 4 where you see that the axle is not there) you should not have any connection at all
measure in that case "A" and "C", and it should be 100K.
I hope you understand it, and that my theory is correct
