If we have a structure that rotates to create artificial gravity, then if the mass isn't perfectly distributed along the circumference the CM will be offset from the geometric center so there will be a wobble.
I made this illustration, to show the wobbles that happens becuse a person goes to visit his/her friend on the opposite side of the structure.
Some artist conceptions include water in the forms of lakes, and are often contiguous bodies of water that circle the entire circumference (Bernal sphere example). If we assume there is a free-flowing body of water around the entire circumference like this (and is sufficiently deep), then it's clear that water will move as a result of a mass movement since the previous water surface is no longer equipotential. This will also move the CM.
How would the presence of water affect the wobble?