Hubble Space Telescope Faint Object Spectrograph (HST FOS) observations have shown that the spectrum of the low-redshift (z(sub em) approximately equal to 0.384) QSO PG 0043+039 exhibits weak broad absorption lines (BALs). The BALs were discovered during the course of UV spectrophotometry made for the HST Quasar Absorption Line Key Project. The HST data are analyzed along with ground-based optical and IUE spectrophotometry. The object is found to have a number of atypical properties relative to normal non-BAL QSOs. The observed continuum is atypical in the sense that it is much weaker than that of a normal optically selected QSO at rest wavelengths approximately less than 2200 A. Intrinsic reddening of E(B-V) approximately equal to 0.11 mag by dust similar to that found in the SMC at the redshift of PG 0043+039 conservatively accounts for the observed continuum shape moderately well. These observed characteristics are typical of low-ionization BAL QSOs, but convincing evidence for BALs due to low-ionization transitions of Mg II, Al III, Al II, or C II does not exist. Therefore, this object may be a misaligned BAL QSO having many of the characteristics of low-ionization BAL QSOs with the sight line passing through a putative dusty region, but evidently missing clouds of high enough column density to produce observable low-ionization BALs. If the intrinsic dust-extinction model is correct, the observations suggest that the dust is not confined to the presumably higher density, low-ionization BAL clouds, but that it has drifted to nearby high-ionization BAL regions. We also consider other possible mechanisms for producing the shape of the continuous energy distribution which cannot be ruled out. We compare the Fe II emission in PG 0043+039 with that in another Key Project QSO, NGC 2841-UB 3, which has optical Fe II emission comparable in strength to that in PG 0043+039, but has anomalously weak UV Fe II emission. In addition, from an analysis of UV and optical spectrophotometric data at 5 epochs over approximately 11 yr, there is tentative evidence that PG 0043+039 has varied in brightness by as much as 1.1 mag during this time interval. Two different interpretations of PG 0043+039 and the low-ionization BAL QSOs are considered. Various model scenarios for explaining the weak narrow-line (O III) emission are considered, but there is no definitive explanation.