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10 pages, 5 figures.-- Under a Creative Commons license., Understanding the ocean carbon sink and its future acidification-derived changes requires accurate and precise measurements with good spatiotemporal coverage. In addition, a deep knowledge of the thermodynamics of the seawater carbonate system is key to interconverting between measured and calculated variables. To gain insights into the remaining inconsistencies in the seawater carbonate system, we assess discrete water column measurements of carbon dioxide fugacity (fCO2), dissolved inorganic carbon (DIC), total alkalinity (TA), and pH measured with unpurified indicators, from hydrographic cruises in the Atlantic, Pacific, and Southern Oceans included in GLODAPv2.2020 (19,013 samples). An agreement of better than ± 3% between fCO2 measured and calculated from DIC and pH is obtained for 94% of the compiled dataset, while when considering fCO2 measured and calculated from DIC and TA, the agreement is better than ± 4% for 88% of the compiled dataset, with a poorer internal consistency for high-CO2 waters. Inspecting all likely sources of uncertainty from measured and calculated variables, we conclude that the seawater carbonate system community needs to (i) further refine the thermodynamic model of the seawater carbonate system, especially K2, including the impact of organic compounds and other acid-base systems on TA; (ii) update the standard operating procedures for the seawater carbonate system measurements following current technological and analytical advances, paying particular attention to the pH methodology that is the one that evolved the most; (iii) encourage measuring discrete water column fCO2 to further check the internal consistency of the seawater carbonate system, especially given the new era of sensor-based seawater measurements; and (iv) develop seawater Certified Reference Materials (CRMs) for fCO2 and pH together with seawater CRMs for TA and DIC over the range of values encountered in the global ocean. Our conclusions also suggest the need for a re-evaluation of the adjustments applied by GLODAPv2 to pH, which were based on DIC and TA consistency checks but not supported by fCO2 and DIC consistency, The research leading to these results was supported through NOAA's Ocean Acidification Program (OAP) via Award #NA17OAR0170332; through NERC via project NE/P021263/1; through the Spanish Research Agency via project PID2019-104279GB-C21/AEI/10.13039/501100011033; and through GAIN via grant IN607A2018/2, With the institutional support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S)