Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble Constant, H 0 . As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1-stellar kinematics, 2-line-of-sight effects, 3deflector mass model. To meet this goal in a quantitative way, we mimic closely the H0LiCOW/SHARP/STRIDES procedures (i.e., TDCOSMO), and we find the following. First, stellar kinematics cannot be a dominant source of error or bias given current uncertainties. Second, we find no bias arising from incorrect estimation of the line-of-sight effects. Third, we show that elliptical composite (stars + dark matter halo), power-law, and cored power-law mass profiles have the flexibility to yield a broad range in H 0 values. However, the TDCOSMO procedures to model the data with both composite and power-law mass profiles are informative. If the models agree, as we observe in real systems owing to the "bulge-halo" conspiracy, H 0 is recovered precisely by both models. If the two models disagreed, as in the case of some pathological models illustrated here, the TDCOSMO procedure would either be able to discriminate between them through the goodness of fit, or account for the discrepancy in the final error bars provided by the analysis. This conclusion is consistent with a reanalysis of the TDCOSMO (real) lenses: the composite model yields H 0 =74.2 +1.6 −1.6 km s −1 Mpc −1 , while the power-law model yields 74.0 +1.7 −1.8 km s −1 Mpc −1 . In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO.