According to the small‐comet hypothesis, small comets strike the Earth approximately 20 times per minute, each small comet nominally containing 100 tons (105 kg) of water‐ice. The primary observations interpreted as evidence for these small comets are dark spots in the Earth's atomic‐oxygen UV dayglow seen by the UV imager on the Dynamics Explorer (DE) satellite. These small comets must disintegrate near Earth and then sublimate within a few seconds, the water vapor expanding to form clouds of water vapor, nominally 50 km in diameter, that temporarily block the spacecraft's view of the dayglow, thus producing the dark spots. In this review we examine problems in basic mechanisms underlying the small‐comet hypothesis. These include inconsistencies with known geophysical phenomena, conflicting results from independent searches for evidence of the presence of small comets, and inconsistencies within the small‐comet hypothesis itself. No other geophysical interpretation that can account for the DE dark spots has been advanced. The only viable alternative in the literature is a nongeophysical one—the instrument‐artifact hypothesis—in which it is proposed that the dark spots appear randomly in the DE pictures. Tests of this hypothesis, both qualitative and statistical, show that it, neatly and economically, explains the DE dark‐spot data. Owing to the weight of accumulated evidence against the small‐comet hypothesis, the lack of credible supporting evidence, and the plausibility of the instrument‐artifact hypothesis, it is unlikely that the small‐comet hypothesis is valid.