  We consider massless three-dimensional $\mathcal{N}=1$ supersymmetric quantum
electrodynamics (QED) with $N_f$ flavours of electrons. Within the dimensional
reduction scheme, we compute the critical exponents corresponding to both the
electron and selectron field and (parity-even) mass anomalous dimensions at the
next-to-leading order in the $1/N_f$ expansion and in an arbitrary covariant
gauge. The equality of the gauge-invariant mass anomalous dimensions of the
electron and the selectron is found to result from a subtle role played by the
epsilon-scalars. Our general framework also allows us to compute the critical
exponents of pure scalar QED and to recover known results in the case of spinor
QED. An application of our results to dynamical (s)electron mass generation is
considered. We find evidence that, while dynamical flavor symmetry breaking
occurs in spinor QED, both pure scalar QED and supersymmetric QED remain in an
interacting conformal phase.
