Using an implementation based on real-space wave functions, we perform G0W0 calculations of the HOMO and LUMO energies of molecules and atoms in the GW100 set. Our main conclusions are as follows: (1) Different implementations of the G0W0 approximation show much better agreements for HOMO (highest occupied molecular orbital) energies than for LUMO (lowest unoccupied molecular orbital) energies. The mean absolute differences between the results calculated with different pseudopotential codes range from 100 to 200 meV. For delocalized LUMOs, all-electron codes that use local orbital basis tend to predict much higher energies than those calculated with plane-wave basis or real-space methods. (2) The effects of semicore electrons in pseudopotentials can explain some of the large discrepancies between results calculated with different GW implementations. For molecules or atoms that include I, Xe, and Ga, pseudopotential-based calculations that exclude semicore electrons produce results that agree better with all-electron calculations. For polar molecules such as NaCl and BrK, however, it is necessary to include semicore electrons for alkaline metal elements to get correct LUMO energies. (3) More than 20 molecules show rearrangement of the order between LUMO (or HOMO) with other orbitals due to GW corrections. Such orbitals that switch order with LUMO are unbound and delocalized in space. The predicted LUMO GW levels (or electron affinity) can be corrected by 2.0 eV if we consider the rearrangement of orbitals in GW calculations. In all, our work clarifies some of the discrepancies between different GW codes and sets a benchmark for real-space implementations of the G0W0 approximation.