The appearance at the end of 2019 of the new SARS-CoV-2 coronavirus led to an unprecedented response by the structural biology community, resulting in the rapid determination of many hundreds of structures of proteins encoded by the virus. As part of an effort to analyze and, if necessary, remediate these structures as deposited in the Protein Data Bank (PDB), this work presents a detailed analysis of 81 crystal structures of the main protease 3CLpro, an important target for the design of drugs against COVID-19. The structures of the unliganded enzyme and its complexes with a number of inhibitors were determined by multiple research groups using different experimental approaches and conditions; the resulting structures span 13 different polymorphs representing seven space groups. The structures of the enzyme itself, all determined by molecular replacement, are highly similar, with the exception of one polymorph with a different inter-domain orientation. However, a number of complexes with bound inhibitors were found to pose significant problems. Some of these could be traced to faulty definitions of geometrical restraints for ligands and to the general problem of a lack of such information in the PDB depositions. Several problems with ligand definition in the PDB itself were also noted. In several cases extensive corrections to the models were necessary to adhere to the evidence of the electron-density maps. Taken together, this analysis of a large number of structures of a single, medically important protein, all determined within less than a year using modern experimental tools, should be useful in future studies of other systems of high interest to the biomedical community.