In-situ layer-by-layer inspection is essential to achieving the full capability and advantages of additive manufacturing in producing complex geometries. The shape of each inspected layer can be described by a 2D point cloud obtained by slicing a thin layer of 3D point cloud acquired from 3D scanning. In practice, a scanned shape must be aligned with the corresponding base-truth CAD model before evaluating its geometric accuracy. Indeed, the observed geometric error is attributed to systematic, random, and alignment errors, where the systematic error is the one that triggers an alarm of system anomalies. In this work, a quickest change detection (QCD) algorithm is applied under a multi-resolution alignment and inspection framework 1) to differentiate errors from different error sources, and 2) to identify the layer where the earliest systematic deviation distribution changes during the printing process. Numerical experiments and a case study on a human heart are conducted to illustrate the performance of the proposed method in detecting layer-wise geometric error.