We present a detailed investigation of the young stellar populations (YSP) in the radio-loud ultraluminous infrared galaxy (ULIRG), PKS 1345+12 (z = 0.12), based on high-resolution Hubble Space Telescope (HST) imaging and long-slit spectra taken with the William Herschel Telescope (WHT) at La Palma. While the images clearly show bright knots suggestive of super star clusters (SSCs), the spectra reveal the presence of YSP in the diffuse light across the full extent of the halo of the merging double nucleus system. Spectral synthesis modelling has been used to estimate the ages of the YSP for both the SSC and the diffuse light sampled by the spectra. For the SSC, we find ages tssc <6 Myr with reddenings 0.2 <E(B - V) <0.5 and masses 106 <MSSCYSP <107M⊙. In the region to the south of the western nucleus that contains the SSC our modelling of the spectrum of the diffuse light is also consistent with a relatively young age for the YSP (∼5 Myr), although older YSP ages cannot be ruled out. However, in other regions of the galaxy we find that the spectra of the diffuse light component can only be modelled with a relatively old post-starburst YSP (0.04-1.0Gyr) or with a disc galaxy template spectrum. The results demonstrate the importance of accounting for reddening in photometric studies of SSC and highlight the dangers of focusing on the highest surface brightness regions when trying to obtain a general impression of the star formation activity in the host galaxies of ULIRGs. The case of PKS 1345+12 provides clear evidence that the star formation histories of the YSP in ULIRGs are complex. While the SSC represent the vigorous phase of star formation associated with the final stages of the merger, the YSP in the diffuse light are likely to represent star formation in one or more of the merging galaxies at an earlier stage or prior to the start of the merger. Intriguingly, our long-slit spectra show line splitting at the locations of the SSC, indicating that they are moving at up to 450 km s-1 with respect to the local ambient gas. Given their kinematics, it is plausible that the SSCs have been formed either in fast moving gas streams/tidal tails that are falling back into the nuclear regions as part of the merger process or as a consequence of jet-induced star formation linked to the extended, diffuse radio emission detected in the halo of the galaxy.