We present the discovery of six millisecond pulsars (MSPs) in the High Time Resolution Universe (HTRU) survey for pulsars and fast transients carried out with the Parkes radio telescope. All six are in binary systems with approximately circular orbits and are likely to have white dwarf companions. PSR J1017-7156 has a high flux density and a narrow pulse width, making it ideal for precision timing experiments. PSR J1446-4701 and PSR J1125-5825 are coincident with gamma-ray sources, and folding the high-energy photons with the radio timing ephemeris shows evidence of pulsed gamma-ray emission. PSR J1502-6752 has a spin period of 26.7 ms, and its low period derivative implies that it is a recycled pulsar. The orbital parameters indicate it has a very low mass function, and therefore a companion mass much lower than usually expected for such a mildly recycled pulsar. In addition we present polarization profiles for all 12 MSPs discovered in the HTRU survey to date. Similar to previous observations of MSPs, we find that many have large widths and a wide range of linear and circular polarization fractions. Their polarization profiles can be highly complex, and although the observed position angles often do not obey the rotating vector model, we present several examples of those that do. We speculate that the emission heights of MSPs are a substantial fraction of the light cylinder radius in order to explain broad emission profiles, which then naturally leads to a large number of cases where emission from both poles is observed.