We present simultaneous spectropolarimetric observations of four visible (630 nm) and three infrared (1565 nm) spectral lines from the German Vacuum Tower Telescope, together with speckle-reconstructed filtergrams in the G-band and the Ca II H line core from the Dutch Open Telescope. After alignment of the data sets, we used the G-band intensity to locate bright points (BPs) in the moat of a regular sunspot. With the cospatial and cotemporal information provided by the polarimetric data, we characterize the magnetic, kinematic, and thermal properties of the BPs. We find that (a) 94% of the BPs are associated with magnetic fields; (b) their field strengths range between 500 and 1400 G, with a rather flat distribution; (c) the contrast of BPs in the G-band depends on the angle between the vector magnetic field and the line of sight; (d) the BPs harbor downflows of magnetized plasma and exhibit Stokes V profiles with large area and amplitude asymmetries; (e) the magnetic interior of BPs is hotter than the immediate field-free surroundings by about 1000 K at equal optical depth; and (f) the mean effective diameter of BPs in our data set is 150 km, with very few BPs larger than 300 km. Most of these properties can be explained by the classical magnetic flux tube model. However, the wide range of BP parameters found in this study indicates that not all G-band BPs are identical to stable long-lived flux tubes or sheets of kG strength. Appendices A-C are only available in electronic form at http://www.aanda.org