The Seismic Experiment for Interior Structure (SEIS) of the InSight mission to Mars has been providing direct information on Martian interior structure and dynamics of that planet since it landed. Compared with seismic recordings on the Earth, ground‐motion measurements acquired by SEIS on Mars are not only made under dramatically different ambient noise conditions, but also include idiosyncratic signals that arise from coupling between different InSight sensors and spacecraft components. This work is to synthesize what is known about these signal types, illustrate how they can manifest in waveforms and noise correlations, and present pitfalls in structural interpretations based on standard seismic analysis methods. We show that glitches (a type of prominent transient signal) can produce artifacts in ambient noise correlations. Sustained signals that vary in frequency, such as lander modes that are affected by variations in temperature and wind conditions over the course of the Martian sol, can also contaminate ambient noise results. Therefore, both types of signals have the potential to bias interpretation in terms of subsurface layering. We illustrate that signal processing in the presence of identified nonseismic signals must be informed by an understanding of the underlying physical processes in order for high‐fidelity waveforms of ground motion to be extracted. Whereas the origins of the most idiosyncratic signals are well understood, the 2.4 Hz resonance remains debated, and the literature does not contain an explanation of its fine spectral structure. Even though the selection of idiosyncratic signal types discussed in this article may not be exhaustive, we provide guidance on the best practices for enhancing the robustness of structural interpretations.