We present a comprehensive symbol error rate (SER) analysis framework for link-level terahertz (THz)-band communication systems under linear zero-forcing (ZF) data detection. First, we derive the mismatched SER for indoor THz systems under independent channel and noise assumptions, calculating the probability density function of the ratio of Gaussian noise to $α$-$μ$ channels resulting from ZF filtering. Next, we derive the precise SER under correlated channel and noise conditions, modeling dependencies using the copula method. Finally, we evaluate the SER for THz channels with correlated distortion noise from hardware impairments. Simulations demonstrate that the proposed framework corrects for multi-dB SERs resulting from the channel-noise independence assumption.