How can I build the tests and ignore any errors

You can run make check with the -i option to ignore errors.

Alternately, you can set the environment variable $HDF5_Make_Ignore to tell the hdf5 Makefile to ignore test errors and continue on. For example:

        env HDF5_Make_Ignore=yes gmake check

When running make check, redirect the output to a file.
If a test fails, make will print a message (echo "*** Error ignored") and continue. Therefore, you can search the output for the string "Error ignored" to see if any tests failed.