After the discovery of Proxima Centauri b in 2016, we observed the system with the Spitzer Space Telescope to look for transits. We confirmed that the planet does not transit. However, we observed three asymmetric, periodic, comet-like events. Unfortunately, we now understand these events to be systematic effects due to telescope vibration, which is occasionally temporally resolved with our 0.02 second frame time. This systematic has been previously identified as a spike in the number of pixels significantly contributing to photometry, but that metric can be misleading. We show that coherent, high-frequency activity in the point-spread function area, measured several ways, is more indicative of this systematic, and that the effect can be partially removed by a quadratic model dependent on point-spread function width. This systematic occurs at an exoplanet-signal level three times in our 80 hours, and more frequently at a lower level, which has implications for transits and eclipses of small and cool planets, respectively. Spitzer is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G.