The non-ideal accuracy and insufficient selectivity of CRISPR/Cas9 systems is a serious problem for their use as a genome editing tool. It is important to select the target sequence correctly so that the CRISPR/Cas9 system does not cut similar sequences. This requires an understanding of how and why mismatches in the target sequence can affect the efficiency of the Cas9/sgRNA complex. In this work, we studied the catalytic activity of the Cas9 enzyme to cleave DNA substrates containing nucleotide mismatch at different positions relative to the PAM in the "seed" sequence. We show that mismatches in the complementarity of the sgRNA/DNA duplex at different positions relative to the protospacer adjacent motif (PAM) sequence tend to decrease the cleavage efficiency and increase the half-maximal reaction time. However, for two mismatches at positions 11 and 20 relative to the PAM, an increase in cleavage efficiency was observed, both with and without an increase in half-reaction time. Thermodynamic parameters were obtained from molecular dynamics results, which showed that mismatches at positions 8, 11, and 20 relative to the PAM thermodynamically stabilize the formed complex, and a mismatch at position 2 of the PAM fragment exerts the greatest stabilization compared to the original DNA sequence. The weak correlation of the thermodynamic binding parameters of the components of the Cas9/sgRNA:dsDNA complex with the cleavage data of DNA substrates containing mismatches indicates that the efficiency of Cas9 operation is mainly affected by the conformational changes in Cas9 and the mutual arrangement of sgRNA and substrates.