Defects in double stranded DNA can arise from damaged bases or mismatched base pairs. In vivo, defects in DNA must be rapidly and efficiently repaired since they affect a variety of cell processes. Here we use molecular dynamics to study the effect of mismatched bps on DNA supercoiling. Under external torsional stress, an elastic rod with a defect would buckle at the defect; provided the defect reduces the local bending stiffness. In genomic DNA however, the entropic cost associated with plectoneme localization could make pinning unfavorable. Magnetic tweezers-based studies of DNA supercoiling have shown that in DNA harboring a single mismatch, the plectoneme always localizes at the mismatch. These studies were conducted at relatively high salt concentrations (>0.5M NaCl). Theoretical studies have predicted that under physiological salt concentrations of ∼0.2M NaCl, plectoneme localization becomes probabilistic. However, both experimental and theoretical approaches are currently limited to positively supercoiled DNA. We develop a simulation framework using the oxDNA model to study the effect of mismatches on both positively and negatively supercoiled DNA in physiologically relevant salt concentrations. We study both positive and negative supercoiling in a 610bp long DNA with 0,2,4 and 6 mismatches at its center. We find that for a positively supercoiled DNA, the oxDNA framework can reproduce the experimentally observed plectoneme pinning at high force (2 pN) and high salt concentrations (1M NaCl). Under physiological salt concentrations (0.2M NaCl), we find that the plectoneme localization at the mismatch becomes probabilistic. To determine the effects of entropy on plectoneme localization directly, we simulate a 1010bp DNA under identical conditions. The utility of the simulation approach is highlighted by the ability to quantify the effect of mismatches on the motion of plectonemes along the DNA molecule.