In this work the spatial resolution and measurement accuracy of the ultrasound diagnostic system at acoustic remote palpation (ARP) using high-intensity focusing ultrasound (HIFU) are studied theoretically and experimentally. A physical model is proposed, which describes the specific features of ARP taking into account the remote nature of ultrasound Doppler probing of the soft tissues local movements, which are caused by the radiation pressure of HIFU pulse. Taking into account the accepted simplifying assumptions it is shown that the model conclusions are in a good agreement with the results of the experiments on measuring the value of displacements under the influence of HIFU. In particular, the nontrivial dependence of the value of displacements, measured by the Doppler method, on the probing depth and focusing degree of the incident and scattered wave beams, is proved. An experimental study was performed on the transverse resolution at ARP in the case of probing of the medium with Young's modulus irregularity, as well as on the influence of noise and interference on the measurement accuracy and resolution. It is concluded, that the transverse resolution at ARP is determined by the parameters of the local area of the movement, and can be significantly higher than the transverse intrinsic resolution of the ultrasound system at B-mode of diagnostics. The obtained results indicate that ARP is a promising method for monitoring the process of the soft tissues thermal ablation, when HIFU is used.