The results of deep long-slit spectroscopy of the extremely low-metallicity blue compact dwarf (BCD) galaxy SBS 0335-052 are presented. Down to intensity levels of 10^{-3 ... -4} of Hbeta, unprecedented for spectroscopy of extra-galactic giant H II regions, we detect numerous weak permitted and forbidden nebular lines in the brightest part of the galaxy. With varying degrees of confidence, the detections include lines of high-ionization ions like Fe^{4+} -Fe^{6+}, implying very hard ionizing radiation. Two broad emission features, possibly from Wolf-Rayet stars, and stellar He II 4200 absorption are seen in the same region. The large spatial extent of He II 4686 emission (implying the presence of sufficient ionizing photons with energies above 54 eV) and the spatial distribution of the electron temperature suggest that at least some part of the hard radiation is associated with shocks. Extended Halpha emission is detected over ~ 6 - 8 kpc, a much larger area than in previous studies, suggesting that hot ionized gas is spread out far away from the central ionizing clusters. This shows that nebular line and continuous emission can significantly modify the colours of these extended regions and must be taken into account in studies of the underlying stellar population.