Bi-spectral retrievals of droplet effective radius and cloud optical depth are widely utilized to estimate aerosol cloud interactions (ACI) in warm clouds in the marine boundary layer. Here, we assess the effect of retrieval errors due to the neglect of 3D radiative transfer during the retrieval process on this analysis of ACI. We use an ensemble of stochastically-modelled cloud fields and 3D radiative transfer simulations to study the retrieval errors at a solar zenith angle of 30. Simulated retrieval biases in droplet number concentration (𝑵𝒅) for all three MODIS channels vary systematically from +35% to -80% as cloud heterogeneity increases. Pixel-level errors can be much larger. Commonly utilized subsampling strategies do not reduce the systematic variation in retrieval error. Negative error correlations between optical depth and droplet effective radius produce spuriously negative slopes between the logarithm of liquid water path and 𝑵𝒅 (-1.0 to -0.3). Pixels at the centre of (8 km)2 patches that are not overcast have a relative bias in 𝑵𝒅 of -50%. The relative frequency of these biased pixels varies linearly with the clear fraction in MODIS data and form the basis for a simple parameterization of 𝑵𝒅 bias that varies with cloud fraction. Using this parameterization, synthetic data experiments indicate that estimates of the first indirect effect in the tropical ocean can be overestimated by up to 30%, and the effect of aerosol on cloud fraction is overestimated by 50%, due to neglecting the correlation between retrieval errors and cloud microphysics.