  A thorough characterization of many samples of the filled skutterudite
compound PrOs4Sb12 is provided. We find that the double superconducting
transition in the specific heat Tc1~1.89K and Tc2~1.72K tends to appear in
samples with a large residual resistivity ratio, large specific heat jump at
the superconducting transition and with the highest absolute value of the
specific heat above Tc1. However, we present evidence which casts doubt on the
intrinsic nature of the double superconducting transition. The ratio of the two
specific heat jumps \Delta C(Tc1)/\Delta C(Tc2) shows a wide range of values on
crystals from different batches but also within the same batch. This ratio was
strongly reduced by polishing a sample down to 120um. Remarkably, three samples
exhibit a single sharp transition of ~15mK in width at Tc~1.7K. The normalized
specific heat jump (C-Cnormal)/Cnormal at Tc of two of them is higher than ~32%
so larger than the sum of the two specific heat jumps when a double transition
exists. As an evidence of better quality, the slope in the transition is at
least two time steeper.
  We discuss the origins of the double transition; in particular we consider,
based on X-ray diffraction results, a scenario involving Pr-vacancies. The
superconducting phase diagram under magnetic field of a sample with a single
transition is fitted with a two-band model taking into account the good values
for the gap as deduced from thermal conductivity measurements.
