This paper explores various sources of error in atmospheric CO2 synthesis inversions using global circulation models. The estimation of prior, observation, model transport, and representation errors is described, and the latter two error sources are explored in more detail. Not accounting for these errors will act as a hard constraint on the inversion and will produce incorrect solutions to the problem as is shown in some example inversions. The magnitude of these errors falls generally between about 10% and 100% in the retrieved fluxes but can be even larger. This makes it highly desirable to avoid hard constraints and apply any prior information we have about the surface fluxes as a weak constraint to the inversion problem.