Any Intel compilers being made available before the compilers in /opt/moose/gcc_4.9.1 may cause some issues. Not sure if there are even compilers in /opt/intel/bin, but its worth mentioning.
Your libMesh config, suggests you have not run the update_and_rebuild_libmesh.sh script after you installed the latest moose package (from your libMesh config.log):
PETSCINCLUDEDIRS='-I/opt/moose/petsc/openmpi_petsc-3.5.2/gcc-opt-superlu/include -I/opt/moose/petsc/openmpi_petsc-3.5.2/gcc-opt-superlu//include -I/opt/moose/petsc/openmpi_petsc-3.5.2/gcc-opt-superlu/include -I/opt/moose/petsc/openmpi_petsc-3.5.2/gcc-opt-superlu/include -I/opt/moose/petsc/openmpi_petsc-3.5.2/gcc-opt-superlu/include -I/opt/moose/openmpi/openmpi-1.8.1/gcc-opt/include'
Your `env` suggests you should be seeing PETSc pointing to: /opt/moose/petsc/openmpi_petsc-3.6.0/gcc-opt-superlu
And the results of `ldd bison-opt` supports this (library not found).
Please note; When ever you re-install the MOOSE environment package, you need to close and re-open all opened terminals. This is necessary to clear out an old environment with possible incorrect PATHs to non-existent things (like PETSc libraries).
What you probably need to do is;
1. cd ~/projects/bison/moose/scripts; ./update_and_rebuild_libmesh.sh
2. cd ~/projects/bison; make clobber
3. make
The `make clobber` command should clean out any stale .o files possibly still wanting to link against those missing PETSc libraries.
Hope this helps!
Jason