A recent study by Farnes (2018, A&A, 620, A92) proposed an alternative cosmological model in which both dark matter and dark energy are replaced with a single fluid of negative mass. This paper presents a critical review of that model. A number of problems and discrepancies with observations are identified. For instance, the predicted shape and density of galactic dark matter halos are incorrect. Also, halos would need to be less massive than the baryonic component, otherwise they would become gravitationally unstable. Perhaps the most challenging problem in this theory is the presence of a large-scale version of the "runaway effect", which would result in all galaxies moving in random directions at nearly the speed of light. Other more general issues regarding negative mass in general relativity are discussed, such as the possibility of time-travel paradoxes. The simulation video is available at http://https://www.aanda.org