Context. Blazars are a subset of active galactic nuclei (AGN) with jets that are oriented along our line of sight. Variability and spectral energy distribution (SED) studies are crucial tools for understanding the physical processes responsible for observed AGN emission. Aims. We report peculiar behavior in the bright γ-ray blazar PKS 1424−418 and use its strong variability to reveal information about the particle acceleration and interactions in the jet. Methods. Correlation analysis of the extensive optical coverage by the ATOM telescope and nearly continuous γ-ray coverage by the Fermi Large Area Telescope is combined with broadband, time-dependent modeling of the SED incorporating supplemental information from radio and X-ray observations of this blazar. Results. We analyse in detail four bright phases at optical-GeV energies. These flares of PKS 1424−418 show high correlation between these energy ranges, with the exception of one large optical flare that coincides with relatively low γ-ray activity. Although the optical/γ-ray behavior of PKS 1424−418 shows variety, the multiwavelength modeling indicates that these differences can largely be explained by changes in the flux and energy spectrum of the electrons in the jet that are radiating. We find that for all flares the SED is adequately represented by a leptonic model that includes inverse Compton emission from external radiation fields with similar parameters. Conclusions. Detailed studies of individual blazars like PKS 1424−418 during periods of enhanced activity in different wavebands are helping us identify underlying patterns in the physical parameters in this class of AGN.