Low-frequency dynamic impedance [σ−1(ω,T)≡(σ1+iσ2)−1] measurements on Josephson junction arrays found that σ1∼|lnω|, σ2∼const. This implies anomalously sluggish vortex mobilities μV(ω)∼σ−11, and is in conflict with general dynamical scaling expressions. We calculate (a) σ(ω,T) by real-space vortex scaling and (b) μV(ω) using Mori's formalism for a screened Coulomb gas. We find, in addition to the usual critical (large-ω) and hydrodynamic (low-ω) regimes, a new intermediate-frequency scaling regime into which the experimental data fall. This resolves the above mentioned conflict and makes explicit predictions for the scaling form of σ(ω,T).