  All the next-to-leading order contributions to the quasi-particle dispersion
laws of a quark-gluon plasma which due to infrared singularities are sensitive
to the magnetic-mass scale are calculated using Braaten-Pisarski resummation.
These relative-order-$g\ln(g)$ corrections are shown here to generally
contribute to the dynamical screening of gluonic fields with frequencies below
the plasma frequency as well as to the damping of propagating gluonic and
fermionic quasi-particles. In the limit of vanishing wave-vector the infrared
singularities disappear, but in a way that raises the possibility for formally
higher orders of the Braaten-Pisarski scheme to equally contribute at
next-to-leading order when the wave-vector is of the order of or less than the
magnetic-mass scale. This is argued to be a problem in particular for the
fermionic damping rate.
