In order to develop and test a methodology to search for UV variability over the entire Galaxy Evolution Explorer (GALEX) database down to the shortest timescales, we analyzed time-domain photometry of ~5000 light curves of ~300 bright (mFUV, mNUV<=14) and blue (mFUV-mNUV<0) GALEX sources. Using the gPhoton database tool, we discovered and characterized instrumentally induced variabilities in time-resolved GALEX photometry that may severely impact automated searches for short-period variations. The most notable artifact is a quasi-sinusoidal variation mimicking light curves typical of pulsators, seen occasionally in either one or both detectors, with amplitudes of up to 0.3mag and periods corresponding to the periodicity of the spiral dithering pattern used during the observation (P~120s). Therefore, the artifact may arise from small-scale response variations. Other artifacts include visit-long "sagging" or "hump" in flux, occurring when the dithering pattern is not a spiral, or a one-time change in flux level during the exposure. These instrumentally caused variations were not reported before, and are not due to known (and flagged) artifacts such as hotspots, which can be easily eliminated. To characterize the frequency and causality of such artifacts, we apply Fourier transform analysis to both light curves and dithering patterns, and examine whether artificial brightness variations correlate with visit or instrumental parameters. Artifacts do not correlate with source position on the detector. We suggest methods to identify artifact variations and to correct them when possible.