We present the discovery and follow-up observations of 142 pulsars found in the Parkes 20-cm multibeam pulsar survey of the Galactic plane. These new discoveries bring the total number of pulsars found by the survey to 742. In addition to tabulating spin and astrometric parameters, along with pulse width and flux density information, we present orbital characteristics for 13 binary pulsars which form part of the new sample. Combining these results from another recent Parkes multibeam survey at high Galactic latitudes, we have a sample of 1008 normal pulsars which we use to carry out a determination of their Galactic distribution and birth rate. We infer a total Galactic population of 30000+/-1100 potentially detectable pulsars (i.e. those beaming towards us) having 1.4-GHz luminosities above 0.1mJy*kpc^2^.