Electrochemical impedance spectroscopy (EIS) measurement, performed in the presence of a redox agent, is a convenient method to measure molecular interactions of electrochemically inactive compounds taking place on the electrode surface. High sensitivity of the method, being highly advantageous, can be also associated with nonspecific impedance changes that could be easily mistaken for specific interactions. Therefore, it is necessary to be aware of all possible causes and perform parallel control experiments to rule them out. We present the results obtained during the early stages of aptamer-based sensor development, utilizing a model system of human alpha thrombin interacting with a thiolated DNA aptamer, immobilized on gold electrodes. EIS measurements took place in the presence of iron ferrocyanides. In addition to known method limitations, that is, inability to discriminate between specific and nonspecific binding (both causing impedance increase), we have found other factors leading to nonspecific impedance changes, such as: (i) initial electrode contamination; (ii) repetitive measurements; (iii) additional cyclic voltammetry (CV) or differential pulse voltammetry (DPV) measurements; and (iv) additional incubations in the buffer between measurements, which have never been discussed before. We suggest ways to overcome the method limitations.