To my knowledge, there is no discretization of the light wavelength (they form a continuous spectrum).
On the other hand, there exists no infinitely narrow absorption "potential". I mean that all transitions of electrons that may correspond to a photon absorption have a finite width. Consequently, the photons have a non-zero probability to get absorbed.
Moreover, many materials do not have narrow energy transitions. For example, metals have free electrons (not bound to an atom, i.e. not subject to atomic transitions) that may absorb many different photon energies. Other materials absorb light through other processes, such as changes in the vibrations of molecules, or in their rotations, etc. These processes show similar transitions to atomic transitions, but these may have much wider wavelength acceptance.
(Another thing to consider: photons do not have a precisely defined wavelength due to Heisenberg uncertainty principle)