Space-based retrievals of column-averaged dry-air mole fractions of CH4 (XCH4), together with chemistry transport models (CTMs), are being used to infer CH4 surface emissions. In these inverse modeling analyses, the estimates of the CH4 surface emissions strongly depend on the fidelity of the atmospheric transport models. However, it is challenging to characterize errors in these atmospheric models. Here we use GOSAT XCH4 retrievals and the GEOS-Chem global CTM, at a horizontal resolution of 4x5 and 2x2.5, to show that space-based XCH4 observations can provide some constraints on model errors. We use a weak constraint four dimensional variational (4D-Var) data assimilation method to identify and partially mitigate the impact of model biases (including transport bias) on the global CH4 distribution. The sensitivity of the observations to different types of model errors is investigated in a set of Observing System Simulation Experiments (OSSEs), where we show that satellite XCH4 retrievals can provide some information on the vertical distribution of model errors. For example, assimilation of the XCH4 observations can mitigate some of the bias in CH4 in the GEOS-Chem stratosphere at high latitudes. More generally, the weak constraint 4D-Var assimilation of XCH4 reveals that the vertical transport over major source regions (such as China) is too weak and will adversely impact inferred CH4 source estimates. Our work shows that although the vertical information in the XCH4 retrievals is limited, there is sufficient information to partially mitigate some of the model errors in the context of the weak constraint 4D-Var assimilation approach.