The recent years have seen a significant development in the use of nonuniform grids for the numerical solution of partial differential equations. In fact, the use of Cartesian meshes composed of rectangular cells does not allow for optimal representation of complex geometries (for example, to handle the presence of cut cells at the boundaries of the computational domain) and, therefore, numerical methods employing either boundary fitted coordinate systems or unstructured grids (finite volumes, finite elements, ...) are a well established way to overcome this problems. Moreover, mesh adaptivity strategies have shown to be very effective in the simulation of physical phenomena, but sometimes their improvements are reduced by the difficulties of modifying the schemes for adapting to nonuniform grids without loosing important features (conservation, well-balancing, ...) This development has given rise to a number of new problems regarding the analysis of approximation algorithms especially because, on nonuniform grids, many formally inconsistent schemes actually converge, in spite of an apparent deterioration of their local truncation error. On the other hand, some consistent methods diverge on nonuniform grids in spite of reducing, when used on uniform grids, to standard convergent schemes. Numerical accuracy on irregular spatial meshes for systems with source terms remains poorly understood, essentially because consistency and accuracy are not anymore related in the usual sense, and a rigorous formulation of consistency for source terms is not an obvious question. 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. Because we are interested in pointing out numerical issues, we present an experimental error analysis to elucidate the influence of the non-uniformity of the mesh mainly on the convergence rates. Precise comments on the limits and potentiality of these approaches are done.