The tolerance of a rotating parallel-mirror-pair spectrometer (RPMPS) and some other considerations are analyzedusing the modulation depth and the phase error criterion.These include the vibration of the parallel-mirror-pair (PMP), the alignment error of the fixed end mirrors, the parallelism of the two rotating mirrors, and the field of view. The theoretical results show that the vibration of the PMP is the most sensitive factor to RPMPS. However, as an ultra rapid continuous rotational system, the rotation inertia will reduce the effect of the vibration dramatically. The RPMPS is less sensitive to the parallelism of the two rotating mirrors. The tolerance for the alignment error of the fixed end mirrors and the field of view are similar to the traditional Michelson interferometer. Compared to the traditional linear motion form spectrometer, the RPMPS is an ultra rapid scanning Fourier-transform spectrometer with stability advantages.These analyses will also give a theoretic guidance for system design and manufacture of RPMPS.