question of "what makes a good mesh" is a fundamental
aspect of the CUBIT mesh generation toolkit. As a result,
significant research has gone into defining quality metrics for
which elements may be judged. Element quality criteria are
generally agreed upon standards for acceptance of a mesh for
VERDICT, a separate module providing these quality criteria, has been developed to help standardize these quality metrics. In addition to providing VERDICT as a linkable software library, a small application known as VERDE has been developed to wrap the VERDICT library. It provides a convenient cross-platform graphical user interface with VTK graphics for visualizing element quality criteria in a mesh.
Sandia's version of the mesh verification library, VERDICT, was released as LGPL open source. It can be downloaded here, along with other open source code developed at Sandia. (Kitware, Inc. is developing a separate BSD licensed version for VTK that's based on Sandia's version. See here for details.)