Criticism of "Necessity of simultaneous co-existence of instantaneous   and retarded interactions in classical electrodynamics" by Andrew E.   Chubykalo and Stoyan J. Vlaev
  The demonstration that the electromagnetic fields derived from the Lienard-Wiechert potentials do not satisfy the Maxwell equations is proved to be false. Errors were made in the computation of the derivatives of retarded quantities. The subsequent inference of the necessity of both instantaneous and retarded electromagnetic interactions cannot be made. Different choices of gauge can lead to a variety of forms for the scalar and vector potentials, always with the same retarded fields. Classical electromagnetic theory is complete as usually expressed. One may choose to work in the Lorenz gauge in which all quantities are retarded. 
J. D. Jackson (Physics, UC Berkeley)