The phrase "serious inconsistency" describes a situation where there is a significant contradiction or disagreement. It means that something doesn't match up or make sense in a significant way. Full definition
Defence lawyer Joseph Neuberger was able to demonstrate to the Crown a number of serious inconsistencies in the statement of the complainant in comparison to other statements obtained through the defence investigation. (nrlawyers.com)
Lack of Consistency Between Modeled and Observed Temperature Trends Energy & Environment, 22, 375 - 406 DOI — 10.1260 / 0958 - 305X.22.4.375 (Not quoted in SOD) drew attention to the fact that «The US Climate Change Science Program [CCSP, 2006] reported, and Douglass et al. [2007] and NIPCC [2008] confirmed, a «potentially serious inconsistency» between modeled and observed trends in tropical surface and tropospheric temperatures.» (wattsupwiththat.com)
«There are serious inconsistencies between Mr Nix's original testimony of 27 February, and evidence received under the inquiry since.» (bbc.com)