The vacuum energy density or free energy of a free charged Bose gas at
non-zero densities is studied in the context of the debate about Multiplicative
Anomalies. Some zeta-function regularised calculations of the free energy in
the literature are reexamined, clarified and extended. A range of apparently
distinct answers can obtained. Equivalent dimensional regularisation results
are also presented for comparison. I conclude that operator ordering and normal
ordering are not responsible for these differences. Rather it is an undesirable
but unavoidable property of zeta-function regularisation which leads to these
different results, making it a bad scheme in general. By comparison I show how
dimensional regularisation calculations give a consistent result without any
complications, making this a good scheme in this context.