  General relativity (GR) has proven to be a highly successful theory of
gravity since its inception. The theory has thrivingly passed numerous
experimental tests, predominantly in weak gravity, low relative speeds, and
linear regimes, but also in the strong-field and very low-speed regimes with
binary pulsars. Observable gravitational waves (GWs) originate from regions of
spacetime where gravity is extremely strong, making them a unique tool for
testing GR, in previously inaccessible regions of large curvature, relativistic
speeds, and strong gravity. Since their first detection, GWs have been
extensively used to test GR, but no deviations have been found so far. Given
GR's tremendous success in explaining current astronomical observations and
laboratory experiments, accepting any deviation from it requires a very high
level of statistical confidence and consistency of the deviation across GW
sources. In this paper, we compile a comprehensive list of potential causes
that can lead to a false identification of a GR violation in standard tests of
GR on data from current and future ground-based GW detectors. These causes
include detector noise, signal overlaps, gaps in the data, detector
calibration, source model inaccuracy, missing physics in the source and in the
underlying environment model, source misidentification, and mismodeling of the
astrophysical population. We also provide a rough estimate of when each of
these causes will become important for tests of GR for different detector
sensitivities. We argue that each of these causes should be thoroughly
investigated, quantified, and ruled out before claiming a GR violation in GW
observations.
