Scientific articles are usually associated with a Digital Object Identifier (DOI). Most publishers request DOIs from Crossref, the largest registration agency that has minted 173 million DOIs to date. The Crossref database stores the metadata of each scholarly work, including its title, authors, as well as references found in the bibliography. Since 2018, Crossref releases monthly dumps of its database amounting to 64 TB in JSON format. Recent integrity issues warrant a complete audit with longitudinal analysis of the Crossref archives. However, auditing is challenging due to the evolving nature of these massive metadata. We introduce an approach to store the complete archives that tracks the history of modifications efficiently. The longitudinal screening of the metadata is illustrated with two indicators designed to detect potential misconducts. We discovered and report two such anomalies involving suspect authors/publishers seemingly gaming citation metrics as well as a previously documented case of fraud involving a journal and its authors. The code is released for reproducibility and to encourage other researchers and Crossref to perform further analyses.