Recent studies of singularities in scalar wave fields in Young’s classic experiment are extended to electromagnetic fields diffracted by an N-pinhole interferometer. Linearly polarized fields whose direction of polarization may be different at each pinhole are examined. It is shown that for two pinholes, only surfaces of linear polarization are created. For N larger than two, a rich structure of polarization singularities is found even when the location of the pinholes is arbitrary. In addition, there can be regions where the spectral density of the field is zero.