We describe the highly variable X-ray and UV emission of V458 Vul (Nova Vul 2007), observed by Swift between 1 and 422 days after outburst. Initially bright only in the UV, V458 Vul became a variable hard X-ray source due to optically thin thermal emission at kT = 0.64 keV with an X-ray band unabsorbed luminosity of 2.3 x 10(34) erg s(-1) during days 71-140. The X-ray spectrum at this time requires a low Fe abundance (0.2(-0.1)(+ 0.3) solar), consistent with a Suzaku measurement around the same time. On day 315 we find a new X-ray spectral component which can be described by a blackbody with temperature of kT = 23(-5)(+9) eV, while the previous hard X-ray component has declined by a factor of 3.8. The spectrum of this soft X-ray component resembles those typically seen in the class of supersoft sources (SSS) which suggests that the nova ejecta were starting to clear and/or that the white dwarf photosphere is shrinking to the point at which its thermal emission reaches into the X-ray band. We find a high degree of variability in the soft component with a flare rising by an order of magnitude in count rate in 0.2 days. In the following observations on days 342.4-383.6, the soft component was not seen, only to emerge again on day 397. The hard component continued to evolve, and we found an anticorrelation between the hard X-ray emission and the UV emission, yielding a Spearman rank probability of 97%. After day 397, the hard component was still present, was variable, and continued to fade at an extremely slow rate but could not be analyzed owing to pile-up contamination from the bright SSS component.