We investigate direct above-threshold ionization in diatomic molecules, with particular emphasis on how quantum interference is altered by a driving field of nonvanishing ellipticity. This interference may be either temporal, i.e., related to ionization events occurring at different times, or spatial, i.e., related to the electron emission at different centers in the molecule. Employing the strong-field approximation and saddle-point methods, we find that, in general, for nonvanishing ellipticity, there will he a blurring of the temporal and spatial interference patterns. The former blurring is caused hy the electron velocity component perpendicular to the major polarization axis, while spatial interference is washed out as a consequence either oïs-p mixing or of the temporal dependence of the ionization prefactor. Both types of interference are analyzed in detail in terms of electron trajectories, and specific conditions for which sharp fringes occur are provided.