Well written and well organized.  Just a few relatively minor comments, the most significant being the question of why CF4 is not included in the analysis.

                Are the molecules indicated in Tables 3 and 4 all the interferers considered in the analysis?  On page 13, line 8, reference is made to H2O, O3, and 14 other species in relation to interferers, but only 14 species appear in the tables (H2O, O3, plus 12 other interferers).  Conspicuously missing is CF4.  The microwindow 1282.5-1283.55 is presumably included because it contains the strong Q-branch of the molecule, and the CF4 signal should extend quite high in altitude (i.e., above the 30 km lower altitude limit of the microwindow).  Excluding it from the analysis would be problematic.

                Also absent is HDO.  I gather differences in isotopologues are generally ignored (both N2O and CH4 have lines from subsidiary isotopologues in the given wavenumber region, which will have slightly different VMR profiles than the main isotopologues), but there are HDO lines in some of the low altitude microwindows (i.e., microwindows that extend down to 6 km), and atmospheric fractionation for HDO relative to the main isotopologue is around a factor of 2 different from the H/D reference factor assumed when scaling HITRAN intensities to isotopic abundance.  If using the same VMR profile as main isotopologue H2O, the HDO signal will be significantly overestimated.  Can that really be ignored in the analysis?

                There are some other molecules that could contribute weakly to the signal in this region (e.g., C2F6), but perhaps those contributions are adequately accounted for by the ‘continuum’ fitting parameters.

                In this wavenumber region, the spectroscopy for HNO3 has been improved in recent years, but there remain missing hot bands in the HITRAN database, which could impact the analysis results.

Page 19: line 16: “We suspect that this bias might be due to the spectroscopic data used”

                Likely a major (maybe the biggest) factor, but not necessarily the only one.  It is perhaps worth noting strong correlations between the CH4 and N2O differences in Figure 8.  Between latitudes 40 S to 40 N and altitudes 10 to 30 km, there is a common pattern: an increase relative to V5 between 10 and 15-20 km, a decrease relative to V5 near 20 km, and an increase relative to V5 between 25 and 30 km.  I gather the two increases worsen the level of agreement with correlative data.  The fact that N2O and CH4 share this pattern suggests a common source for the differences, something mechanical in the retrieval (changes in tangent heights, changes in pressure and temperature profiles, etc.).  This in turn suggests there could be contributions to the biases other than just spectroscopy.

Minor issues:

Page 2, line 32: a formatting issue (truncated sentence that is continued on the next page).

Page 16, line 21: “even some more”

                even more

The paper is well written and well suited for AMT. I'd suggest publication after a few minor corrections, listed below.

Page 1, lines 4-5: “…with respect to the atmospheric state variables jointly retrieved with the target gases CH₄ and N₂O…” is awkwardly phrased. Does this mean that CH₄ and N₂O are now retrieved simultaneously and weren’t previously?

Page 2, line 18: “Submillimeter Wave Radiometer” should be “Sub-Millimetre Radiometer” (note the spelling of sub-millimetre)

Page 3, line 30: Please specify what the high bias is with respect to

Page 5, lines 14-16: I assume you mean H₂O and HNO₃ are interfering species that are no longer joint-fitted. If so, please clarify in the text. Also, please explain what is meant by “hardly any influence”

Section 3.1.2: Please briefly explain the physical justification for how the radiance offset could be altitude-dependent?

Page 8, line 11: If CO₂ is an interfering species, why isn’t its VMR listed as an uncertainty in Table 3?

Page 17, line 4: for consistency, “methane” should probably be “CH₄”

Page17, line 8: it seems a bit odd to be using vague phrases like “had been as high as” and “could be reduced to” and then give very specific values. Why not just give the rates for both V5 and V8 (as done in the next sentence), or say the version that had a non-convergence rate of 8.4%?

Figure 6: in my opinion, there’s more data here than necessary, which makes it difficult to see the region of interest. Maybe consider only showing the northern latitudes to highlight the oscillations better.

See supplement.