The Nordic Near-Earth Object Network (Nordic NEON) observing program was established to obtain knowledge of the physical and dynamical properties of near-Earth objects (NEOs). Photometric and astrometric observations have been carried out at the Nordic Optical Telescope since June 2004. By collaborating with other observing programs and applying for observing time from other telescopes (e.g. European Southern Observatory), we aim at significantly increasing the knowledge of the physical and dynamical properties of NEOs by using novel inverse methods. For many targets with previously published spin solutions we cannot, in reality, get a single solution based on existing data, but there exist a large number of possible solutions none of which can be given priority over the others. Currently, distributions of possible pole directions and shapes have been derived for four new asteroids (2002 FF12, 2003 MS2, 2003 RX7, 2004 HW) as well as for 1685 Toro and 1981 Midas. For 1862 Apollo, we have obtained an unambiguous spin and shape solution. Following the so-called statistical inversion theory and focussing on 2004 AS1 that once posed an imminent impact hazard some 48 hours after discovery, we illustrate the challenges in assessing the collision probabilities of NEOs with exiguous observational data. Finally, we describe an orbit computation method utilizing the full six-dimensional phase-space volume of variation for objects with moderate observational data, underscoring its future prospects in collision probability computations.