  The Planck list of high-redshift source candidates (the PHz catalogue)
contains 2151 peaks in the cosmic infrared background, unresolved by Planck's 5
arcmin beam. Follow-up spectroscopic observations have revealed that some of
these objects are $z \approx 2$ protoclusters and strong gravitational lenses,
but an unbiased survey has not yet been carried out. To this end, we have used
archival Herschel-SPIRE observations to study a uniformly-selected sample of
187 PHz sources. In contrast with follow-up studies that were biased towards
bright, compact sources, we find that only one of our PHz sources is a bright
gravitationally-lensed galaxy (peak flux $\gtrsim 300$ mJy), indicating that
such objects are rarer in the PHz catalogue than previously believed ($< 1$ per
cent). The majority of our PHz sources consist of many red, star-forming
galaxies, demonstrating that typical PHz sources are candidate protoclusters.
However, our new PHz sources are significantly less bright than found in
previous studies and differ in colour, suggesting possible differences in
redshift and star-formation rate. Nonetheless, 40 of our PHz sources contain $>
3\sigma$ galaxy overdensities, comparable to the fraction of $> 3\sigma$
overdensities found in earlier biased studies. We additionally use a
machine-learning approach to identify less extreme (peak flux $\sim 100$ mJy)
gravitationally-lensed galaxies among Herschel-SPIRE observations of PHz
sources, finding a total of seven candidates in our unbiased sample, and 13
amongst previous biased samples. Our new uniformly-selected catalogues of $>
3\sigma$ candidate protoclusters and strong gravitational lenses provide
interesting targets for follow up with higher-resolution facilities, such as
ALMA and JWST.
