I obtain the following error at the end of my program:

   *** The MPI_Comm_free() function was called after MPI_FINALIZE was invoked.
   *** This is disallowed by the MPI standard. 
   *** Your MPI job will now abort. 

What should I look for to resolve this issue?

Make sure that all open objects are closed before calling MPI_FINALIZE. This includes not just the file, groups, and datasets, but also property lists, dataspaces, etc. If you are sure that all objects are closed and you still get this error, then please send an example program that reproduces the issue to the The HDF Helpdesk.