Do the center of mass and the center of gravity coincide for a building? for a lake? Under what conditions does the difference between the center of mass and the center of gravity be- come significant? Give an example.

The center of mass depends upon the distribution of the mass of the object while the center of object depends on the distribution of weight. Therefore in situations where the acceleration due to gravity does not remain constant for every particle in object, the center of gravity will not coincide with the center of mass.
If the building is assumed to be symmetrical, the center of the mass will lie on the geometric center. However, if the building is tall enough that the acceleration due to gravity experienced by the particles is different at different locations, the center of gravity would move away from the center of mass.
In case of lake, one can approximate that the center of gravity will coincide with the center of mass if the water is symmetrically distributed and the acceleration due to gravity at every point is also same.