  We use recent advances in the local evaluation of Brauer elements to study
the role played by {\it odd} torsion elements of the Brauer group in the
arithmetic of diagonal quartic surfaces over {\it arbitrary} number fields. We
show that over a local field if the order of the Brauer element is odd and
coprime to the residue characteristic then the evaluation map it induces on the
local points is constant. Over number fields we give a sufficient condition on
the coefficients of the equation, which is mild and easy to check, so that the
odd torsion does not obstruct weak approximation. We also note a systematic way
to produce $K3$ surfaces over $\Q_2$ with good reduction and a non-trivial
2-torsion element of the Brauer group with Swan conductor zero.
