Imaging static Fourier transform spectrometry (isFTS) is used for pushbroom airborne or spaceborne hyperspectral remote sensing. In isFTS, a static two-wave interferometer imprints linear interference fringes over the image of the scene, so that the spectral information is multiplexed over several instantaneous images, and numerical reconstruction is needed to recover the full spectrum for each pixel. The image registration step is crucial since insufficient accuracy leads to artefacts on the images and the estimated spectra. In order to investigate these artifacts, we performed a theoretical study and designed a simulation program. We established that registration errors create crenellated spatial patterns, the magnitude of which depends on the radiance gradient of the scene, the amplitude of the registration error, and the wavelength. In the case of sinusoidal perturbations, which may correspond for instance to mechanical vibrations of the carrier, we established that spurious peaks appear on the spectrum, similarly to what happens in dynamic FTS, but with spatial patterns specific to static interferometers.