Josephson junctions can serve as mixers for electromagnetic radiation, producing difference frequencies vertical bar mf(s)-nf(LO)vertical bar of the signal frequency f(s) and the local oscillator frequency f(LO), where the latter can be provided by ac Josephson currents, and m and n are natural numbers. In order to obtain a better understanding of the purity of the terahertz radiation generated by stacks of intrinsic Josephson junctions (IJJs), we study self-mixing-i.e., f(s) is also produced by Josephson currents inside the stacks-in the difference-frequency range between 0.1 and 3.0 GHz. Simultaneously, we perform off-chip terahertz emission detection and transport measurements. We find that at high-bias currents, when a hot spot has formed in the stack, the power level of self-mixing can be low and sometimes is even absent at the terahertz emission peak, pointing to a good phase locking among all IJJs. By contrast, at low-bias currents where no hot spot exists, the self-mixing products are pronounced even if the terahertz emission peaks are strong. The mixing products at high operation temperature, at which the temperature variation within the stack is moderate, are minor, indicating that the low junction resistance, perhaps in combination with the lowered Josephson critical current density, may play a similar role for synchronization as the hot spot does at low temperature. While these observations are helpful for the task to synchronize thousands of IJJs, the observation of self-mixing in general may offer a simple method in evaluating the coherence of terahertz radiation produced by the IJJ stacks.