The recent years have seen a significant development in the use of nonuniform grids for the numerical solution of partial differential equations. This development has given rise to a number of new problems regarding the analysis of such methods: firstly, on nonuniform grids, many formally inconsistent schemes converge. We shall report on a numerical study of the properties of supra-convergence for hyperbolic conservation laws with geometrical source terms, which has confirmed that the standard consistency condition for the numerical fluxes do not guarantee that the (local) truncation error vanishes in presence of nonuniform meshes. Nevertheless, the main issue of an error analysis with optimal rates can be pursued, by virtue of the results obtained on the supra-convergence phenomenon for numerical approximation of hyperbolic conservation laws. More clearly, despite the fact that a deterioration of the point-wise consistency is observed in consequence of the non-uniformity of the mesh, the formal accuracy of the methods is actually maintained as the global error behaves better than the truncation error would indicate. This property of enhancement of the numerical error has been widely explored for homogeneous problems, and we attempt at extending such theory to conservation laws with geometrical source terms that are discretized by means of well-balanced schemes, as suggested by the classical application to the Saint-Venant equations for shallow waters. It is worth remarking that the results announced above cannot affect the case of ordinary differential equation with parameter-dependent (geometrical) source terms, namely for systems with negligible fluxes. In effects, elementary counter-examples show that (strong) convergence fails for nonuniform grids, and then some specific approach has to be designed for recovering the error analysis for finite volume schemes on nonuniform meshes. Precise comments on the limits and potentiality of these approaches will be done.