The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) RbMnF3 has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range 0.77T(N) < T < 1.11T(N), where T-N is the Neel temperature. In agreement with previous measurements, at T-N and for wave vectors away from the AF zone center, the scattering has a quasielastic component in addition to the inelastic response predicted by renormalization-group and mode-coupling theories. Both components scale with the dynamic exponent z = 1.43 +/- 0.04, in agreement with dynamic scaling. On cooling below T-N the inelastic peaks transform into the transverse spin waves and a crossover has been observed in the dispersion from a power-law relation omega(q) = Aq(z) at T-N to a linear behavior omega(q) = cq in the hydrodynamic region below T-N. The quasielastic component evolves below T-N into the longitudinal susceptibility identified in an earlier polarized neutron experiment. The intensity and energy width of the longitudinal scattering decrease on cooling below T-N. Down to the lowest temperatures where the longitudinal susceptibility could be measured the leading term in the scaling behavior of the energy width was gamma(q) approximate to q(1.58+/-0.03) (hydrodynamic theory predicts a q(2) law). Possible explanations for the observed behavior of the longitudinal susceptibility are discussed.