Exploiting the millimeter wave (mmWave) band has recently attracted considerable attention as a potential solution to widespread deployment of device-to-device (D2D) communication challenges, namely, spectrum scarcity and interference. However, its directional nature makes the utilization of mmWave band a challenging task as it requires careful beam alignment between the D2D transmitter and receiver. In this paper, we investigate the impact of inaccurate angle-of-arrival (AoA) estimation as a beam alignment impairment on the performance of a directional mmWave D2D network. We have used tools from stochastic geometry to quantify the signal-to-interference-plus-noise ratio (SINR) coverage probability in the presence of beam misalignment, which can be applied to evaluate D2D network performance. Moreover, the analytical results are verified to be reliable and effective through extensive simulations. Finally, the coverage probability of the D2D network with erroneous beam alignment is compared to the network with perfect beam alignment. The numerical results indicate that the beam misalignment can lead to significant losses in the network's coverage probability.