<p>Improving the accuracy of measurements in the dynamic goniometry is closely connected with attainment of the ultimate accuracy of the optical null indicator. This device is included in the composition of angle-measuring devices operating on the principle of a&#xa0;dynamic goniometer. The autocollimator-null-indicator generates an electric pulse when its optical axis coincides with the normal to the controlled reflecting surface. This pulse is used to take the readings of the angular scale of dynamic goniometer. The ultimate accuracy of the autocollimator-null-indicator is determined by its random error. The random error of measurements of the constant angular position of a&#xa0;reflecting mirror was experimentally investigated at different times of the day. It was demonstrated that external noises are predominant in the data of daytime measurements; these are various vibrations, fluctuations of air and external illumination, which depend on the distance between the autocollimator-null-indicator and the mirror. At the same time, in the nighttime measurements, the influence of external actions on the measurement data is minimal, which enables one to get nighttime measurement errors on the level of flicker noise. The experimental data are analyzed by the methods of mathematical statistics, Allan variance, and wavelet analysis. It is shown that the arrays of random variables characterizing the random error are nonstationary. The minimum value of the random error for the autocollimator-null-indicator is equal to 0.001″. The accumulated results are of interest for experts involved in the development and application of optoelectronic devices based on the autocollimators.</p>