The Chang’E-2 digital elevation model (DEM, named CE2TMap2015), which is the highest resolution DEM product in China, was released with global coverage of the lunar surface. A detailed geometric quality assessment of the product is desirable for wider applications by users. A novel procedure for evaluating DEM geometric quality, which investigates both the global geometric uncertainty and local gross errors, is proposed in this paper. First, the DEM was divided into regular blocks and matched with the reference DEM. Then, the characteristics of errors were investigated using the statistical information of the matched tie points. Next, the local outlier factor (LOF) algorithm was performed to locate the gross errors. In our experiment, CE2TMap2015 was evaluated using the proposed method, with SLDEM2015 as the reference DEM. The results show that there were widespread geometric inconsistencies with an area-weighted average of 183.1 m horizontally (with the standard deviation being 101.2 m) and 2.3 m vertically (with the standard deviation being 15.4 m). Gross errors were detected automatically and were excluded in the statistical analysis. The periodic errors were extracted in the frequency domain using a Fourier transform. Our research results provide instructional information for the utilization of CE2TMap2015 by world-wide users. The proposed method can be used in the assessment of other planetary DEMs.