Dipole polarizabilities and C6 and C9 dispersion coefficients are computed for closed- and open-shell atoms and molecules, using dynamic (time-dependent) density functional (TD-DFT) linear response theory as implemented in the response module of the NWChem quantum chemistry package. The response module is capable of accurate calculations of these properties, based on spin-restricted and spin-unrestricted formalisms. The calculated static polarizabilities and dispersion coefficients are compared to available experimental and other theoretical data. The behavior of the dynamic polarizability at imaginary frequencies is analyzed for differently sized closed- and open-shell systems. An interpolation method enforcing the monotonic decrease of the polarizability with increasing imaginary frequency is beneficial for the integration used to obtain C6 and C9. Scaling of the TD-DFT data by ratios of the static polarizability, which can be calculated with a variety of methods, including highly accurate theories, may be used as a leading-order correction.