We present results from an analysis of FUSE spectroscopy of the z_em = 0.57 quasar PKS 0405-123. We focus on the intervening metal-line systems identified along the sight line and investigate their ionization mechanism, ionization state, and chemical abundances. Including Hubble Space Telescope STIS spectroscopy, we survey the entire sight line and identify six O VI absorbers to a 3 σ equivalent width (EW) limit of 60 mÅ. This implies an incidence dN/dz = 16 consistent with previous O VI studies. In half of the O VI systems we report positive detections of C III, suggesting that the gas is predominantly photoionized, has multiple ionization phases, or is in a nonequilibrium state. This contrasts with the general description of the warm-hot intergalactic medium (WHIM) as described by numerical simulations in which the gas is predominantly in collisional ionization equilibrium. An appreciable fraction of O VI absorbers may therefore have a different origin. We have also searched the sight line for the Ne VIII doublet (a better probe of the WHIM at T > 10⁶ K) over the redshift range 0.2 < z < z_em. We report no positive detections to an EW limit of 80 mÅ, giving dN/dz < 40 at 95% c.l. The photoionized metal-line systems exhibit a correlation between the ionization parameter (U ≡ Φ/cn_H, with Φ the flux of hydrogen ionizing photons) and H I column density for N(H ) = 10¹⁴-10¹⁶ cm^-2. Both the slope and normalization of this correlation match the prediction inferred from the results of Davé and Tripp for the low-z Lyα forest. In turn, the data show a tentative, unexpected result: five out of the six photoionized metal-line systems show a total hydrogen column density within a factor of 2 of 10^18.7 cm^-2. Finally, the median metallicity [M/H] of twelve z ~ 0.3 absorbers with N(H ) > 10¹⁴ cm^-2 is [M/H] > -1.5, with large scatter. This significantly exceeds the median metallicity of C IV and O VI systems at z ~ 3 and indicates enrichment of the intergalactic medium over the past ≈10 Gyr.