We analyze total and polarized intensity images of the quasar PKS 0420-014 obtained monthly with the VLBA at 43 GHz during 2008-2012 along with γ-ray data provided by the Fermi Large Area Telescope and multi-color photometric and polarimetric measurements collected by different optical telescopes. During this period the quasar underwent a number of optical flares, which were accompanied by rapid rotation of polarization angle, an increase of activity in γ-rays, and the appearance of new superluminal knots in the parsec-scale jet. We investigate the fine structure of the flares at different wavelengths and in polarized light, and determine kinematic parameters of the knots. We compare the rapid evolution of the optical polarization with the polarization of the VLBI core and knots. We interpret the multi-wavelength behavior within a model that places the blazar "dissipation zone" at the millimeter-wave core of the parsec-scale jet. © Owned by the authors, published by EDP Sciences, 2013.