RISA News has published an article on why plate meshing is important. Basic understanding proper plate meshing is required to get reliable results on or Finite Element Mesh. Without proper meshing of plates, inaccurate results are sure to follow. Their example shows how too coarse of a mesh can result in stresses that are only half the magnitude of the actual solution.
As a rule of thumb, if the results change by less than 10% when doubling your mesh you can probably stop submeshing at that point.