The frequency-dependent complex optical conductivity σ ̂ ( f ) reflects key properties of superconductors, such as the energy gap 2 Δ in the density of states (DOS) and the superfluid density n s . For disordered superconductors, σ ̂ ( f ) often can be described within Bardeen-Cooper-Schrieffer (BCS) theory, while in corresponding tunneling experiments, deviations in the observed DOS typically require modeling by the phenomenological Dynes formula. The implications of such Dynes DOS for optics have been rarely discussed so far. Here we probe the terahertz σ ̂ ( f ) of superconducting NbN thin films with thicknesses ranging from 4.5 to 20 nm, which were grown by atomic layer deposition. Our frequency range from 0.3 to 2.1 THz covers energies below and above 2 Δ . For 20-nm-thick NbN, we find in σ ̂ ( f ) distinct deviations from the BCS model, including a steplike characteristic in the absorption at Δ 0 , i.e., half the zero-temperature spectral gap. These observations can be fully captured by introducing a small and temperature-independent Dynes pair-breaking rate Γ ∼ 0.036 Δ 0 . For the other films, we also observe signs of Dynes-type DOS and we discuss the evolution of 2 Δ 0 , n s , 0 , and Γ as a function of film thickness.