Define "funny readings".
Here's what I would do. I test things for a living, and I've installed dozens of pots in guitars and pedals (and even cooked a few

). First, de-solder all wires from the pot, then do the following tests:
1. Measure the resistance between the two outside lugs of the pot. It should be close (+/- 20%) to the pot's spec value. If it's infinity, zero, or way off, you cooked the pot. If it's normal, continue.
2. Turn the pot all the way to one side. Measure the resistance between the center lug and the lug on that side. If it's more than zero, you cooked the pot. Otherwise, turn the pot all the way to the other side and measure between the center and that side. If both sides read zero, continue.
3. Measure the resistance between the back of the pot and each of the lugs. If any of them read anything other than infinity, you cooked the pot.
If all these tests pass, the pot is probably fine.