This letter derives bounds on performance degradation due to measurement noise in millimeter wave beam alignment methods that train a subset of beam pairs. The analysis applies the union bound and pairwise beam selection error for a wideband channel. While the analysis is oblivious to the method to select the subset of beam pairs, inverse fingerprinting beam alignment is used as a concrete numerical example. Performance evaluation results for different bandwidths show that a wideband system suffers less from measurement noise with the same training sequence duration.