This paper provides an update of our previous scaling relations between galaxy-integrated molecular gas masses, stellar masses, and star formation rates (SFRs), in the framework of the star formation main sequence (MS), with the main goal of testing for possible systematic effects. For this purpose our new study combines three independent methods of determining molecular gas masses from CO line fluxes, far-infrared dust spectral energy distributions, and similar to 1 mm dust photometry, in a large sample of 1444 star-forming galaxies between z = 0 and 4. The sample covers the stellar mass range log(M-*/M-circle dot) = 9.0-11.8, and SFRs relative to that on the MS, delta MS = SFR/SFR (MS), from 10(-1.3) to 10(2.2). Our most important finding is that all data sets, despite the different techniques and analysis methods used, follow the same scaling trends, once method-to-method zero-point offsets are minimized and uncertainties are properly taken into account. The molecular gas depletion time t(depl), defined as the ratio of molecular gas mass to SFR, scales as (1 + z)(-0.6) x (delta MS)(-0.44) and is only weakly dependent on stellar mass. The ratio of molecular to stellar mass mu(gas) depends on (1+ z)(2.5) x (delta MS)(0.52) x (M-*)(-0.36), which tracks the evolution of the specific SFR. The redshift dependence of mu(gas) requires a curvature term, as may the mass dependences of t(depl) and mu(gas). We find no or only weak correlations of t(depl) and mu(gas) with optical size R or surface density once one removes the above scalings, but we caution that optical sizes may not be appropriate for the high gas and dust columns at high z.