  We identify and investigate the nature of the 20 brightest 250-micron sources
detected by the BLAST within the central 150 sq. arcmin of the GOODS-South
field. Aided by the available deep VLA radio imaging, reaching S_1.4 = 30
micro-Jy, we have identified radio counterparts for 17/20 of the 250-micron
sources. The resulting enhanced positional accuracy of ~1 arcsec has then
allowed us to exploit the deep multi-frequency imaging of GOODS-South to
establish secure galaxy counterparts for the 17 radio-identified sources, and
plausible galaxy candidates for the 3 radio-unidentified sources. Confusion is
a serious issue for this deep BLAST 250-micron survey, due to the large size of
the beam. Nevertheless, we argue that our chosen counterparts are significant,
and often dominant contributors to the measured BLAST flux densities. For all
of these 20 galaxies we have been able to determine spectroscopic (8) or
photometric (12) redshifts. The result is the first `complete' redshift
distribution for a deep 250-micron selected galaxy sample. This reveals that
250-micron surveys reaching detection limits of ~30 mJy contain not only
low-redshift spirals/LIRGs, but also the extreme z~2 dust-enshrouded starburst
galaxies previously discovered at sub-millimetre wavelengths. Based on their
IRAC colours, we find that virtually all of the BLAST galaxy identifications
appear better described as analogues of the M82 starburst galaxy, or Sc
star-forming discs rather than highly obscured ULIRGs. Inspection of the LABOCA
870-micron imaging of the GOODS-South field yields detections of 7/11 of the
z>1 BLAST sources, and reveals 250/870 flux-density ratios consistent with a
standard 40K modified black-body fit with a dust emissivity index beta=1.5.
