One popular approach to assess the geometric differences between a part produced by additive manufacturing (AM) and its intended design is the use of a 3D scanner to produce a point cloud. This digital scan is then aligned against the part’s intended design, allowing for quantification of print accuracy. One of the most common methods for achieving this alignment is the Iterative Closest Point (ICP) algorithm. This paper evaluates several potential pitfalls that can be encountered when applying ICP for assessment of dimensional accuracy of AM parts. These challenges are then illustrated using simulated data, allowing for quantification of their impact on the accuracy of deviation measurements. Each of these registration errors was shown to be significant enough to noticeably affect the measured deviations. An efficient and practical method to address several of these errors based on engineering informed assumptions is then presented. Both the proposed method and traditional unconstrained ICP are used to produce alignments of real and simulated measurement data. A real designed experiment was conducted to compare the results obtained by the two registration methods using a linear mixed effects modeling approach. The proposed method is shown to produce alignments that were less sensitive to variation sources, and to generate deviation measurements that will not underestimate the true shape deviations as the unconstrained ICP algorithm commonly does.