We performed wave-optics-based numerical simulations at mid-infrared wavelengths to investigate how the presence or absence of entrance slits and optical aberrations affect the spectral resolving power R of a compact, high-spectral-resolving-power spectrometer containing an immersion-echelle grating. We tested three cases of telescope aberration (aberration-free, astigmatism, and spherical aberration), assuming the aberration budget of the Space Infrared Telescope for Cosmology and Astrophysics, which has a 20     μm wavelength diffraction limit. In cases with a slit, we found that the value of R at around 10 to 20  μm is approximately independent of the assumed aberrations, which is significantly different from the prediction of geometrical optics. Our results also indicate that diffraction from the slit improves R by enlarging the effective illuminated area on the grating window and that this improvement decreases at short wavelengths. For the slit-less cases, we found that the impact of aberrations on R can be roughly estimated using the Strehl ratio.