Ages, chemical compositions, velocity vectors, and Galactic orbits for stars in the solar neighbourhood are fundamental test data for models of Galactic evolution. The Geneva-Copenhagen Survey of the Solar neighbourhood (Nordstrom et al. 2004A&A...418..989N; GCS), a magnitude-complete, kinematically unbiased sample of 16,682 nearby F and G dwarfs, is the largest available sample with complete data for stars with ages spanning that of the disk. We aim to improve the accuracy of the GCS data by implementing the recent revision of the Hipparcos parallaxes. The new parallaxes yield improved astrometric distances for 12,506 stars in the GCS. We also use the parallaxes to verify the distance calibration for uvbyHbeta photometry by Holmberg et al. (2007A&A...475..519H; GCS II, Cat. VI/117). We add new selection criteria to exclude evolved cool stars giving unreliable results and derive distances for 3,580 stars with large parallax errors or not observed by Hipparcos. We also check the GCS II scales of T_eff_ and [Fe/H] and find no need for change. From the new distances we compute revised Mv, U, V, W, and Galactic orbital parameters for 13,520 GCS stars. We also recompute stellar ages with the new values of Mv from the Padova stellar evolution models used in GCS I-II, and compare them with ages from the Yale-Yonsei and Victoria-Regina models. Finally, we compare the observed age-velocity relation in W with three simulated disk heating scenarios to show the potential of the data. With these revisions, the basic data for the GCS stars should now be as reliable as is possible with existing techniques. Further improvement must await consolidation of the T_eff_ scale from angular diameters and fluxes, and the Gaia trigonometric parallaxes. We discuss the conditions for improving computed stellar ages from new input data, and for distinguishing different disk heating scenarios from data sets of the size and precision of the GCS.