This study presents an error analysis of a specific single-frame dual-quaternion batch estimator that employs point and unit vector measurements. The estimator addresses a constrained least-squares optimization by minimizing a cost function that aggregates orientation and position errors. An eigenvalue-based error analysis is developed for the first time for that dual quaternion estimator, yielding closed-form expressions for the three-dimensional attitude and translation error vectors and their covariance matrices. Extensive Monte Carlo simulations validate the accuracy of these analytical predictions.