  We exploit the Seiberg-Witten maps for fields and currents in a U(1) gauge
theory relating the noncommutative and commutative (usual) descriptions to
obtain the O(\theta) structure of the commutator anomalies in noncommutative
electrodynamics. These commutators involve the (covariant) current-current
algebra and the (covariant) current-field algebra. We also establish the
compatibility of the anomalous commutators with the noncommutative covariant
anomaly through the use of certain consistency conditions derived here.
