At 12 V across it, that resistor should be at least 2 W, 4 W or more would be better. The resistor should be labeled. Assuming it has leads, it should be the diameter of a pencil or larger.
My concern focuses on your problem statement. Namely, that the power supply worked fine until you "fixed" wires attached to the potentiometer. That is where I would look for problems, and without knowing what the potentiometer does or how the wires are attached to it we will all be at a loss.