Deuteron jumps along hydrogen bonds in KD2PO4 associated with effective motion of Slater-Takagi DPO4 and D3PO4 groups are related to the deuteron magnetic-resonance spectrum and relaxation both above and below the ferroelectric transition temperature Tc, and to the dielectric relaxation and the domain-wall mobility. Below Tc the deuterons assume ordered bond positions, but occasionally jump to the opposite positions. The correlation time for the electric-field-gradient fluctuations seen by a deuteron undergoing such motion is found to be short above Tc and even shorter below Tc. The rms amplitude of the fluctuations drops rapidly below Tc. These results are used to explain the temperature dependence of the splitting and lack of line broadening in the deuteron spectrum below Tc, and the rapid decrease of the spin-lattice transition probabilities below Tc. Relaxation data above Tc, which yielded the energies and fractional populations of DPO4 and D3PO4 groups, are reanalyzed using the recently reported field-gradient tensors at the two bond positions. The dielectric relaxation is calculated, and good agreement with the high dielectric loss measured at microwave frequencies is found. The jump time for a DPO4 or D3PO4 group is found to be near hkT, implying little correlation between successive jumps, in contrast to KH2PO4. This jump time is used in a calculation of domain-wall mobility in KD2PO4.