How can I test if the burr is aligned properly?

Turn the grind adjustment ring to the setting where the burrs begin lightly touching (likely a 2). With a sharpie or pencil, find the spot where the inner and outer burrs touch and mark the spot on both burrs.

Remove the thumbnut and pull off the inner burr. Turn the burr 180 degrees and replace the inner burr on the axle (the marks on the inner and outer burr should be on opposite sides). Are the burrs still touching in the same place, or did the contact point move?
If they are still touching in the same place (the point where the outer burr is marked), then the problem is the axle or outer burr. If the contact point moved, then the problem is the inner burr.