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Deriving aerosol optical depth (AOD) from space-borne observations is still challenging due to uncertainties associated with sensor calibration drift, cloud screening, aerosol type classification, and surface reflectance characterization. As an initial step to understanding the physical processes impacting these uncertainties in satellite AOD retrievals, this study outlines a theoretical approach to estimate biases in the satellite aerosol retrieval algorithm affected by surface albedo and prescribed aerosol optical properties using a simplified radiative transfer model with a traditional error propagation approach. We expand the critical surface reflectance concept to obtain the critical surface albedo (CSA), critical single scattering albedo (CSSA), and critical asymmetry parameter (CAP). The top-of-atmosphere (TOA) reflectance is not sensitive to significant variability in aerosol loading (AOD) at the critical value; thus, the AOD cannot be determined. Results show that 5% bias in surface albedo (A), single scattering albedo (SSA), or asymmetry parameter (g) lead to large retrieved AOD errors, especially high under conditions when A, SSA, or g are close to their critical values. The results can be useful for future research related to improvements of satellite aerosol retrieval algorithms and provide a preliminary framework to analytically quantify AOD uncertainties from satellite retrievals.