The large scale structure and physics of molecular gas in the Galactic center region is discussed based on the detailed analysis of a 9' resolution survey of the Galactic center region in the J = 1 -> 0 line of C18O. Emphasis is placed on the comparison with 12CO(1-0) data. The line shapes of C18O(1-0) and 12CO(1-0) differ significantly. The ratio of the intensities of the two isotopomers in the Galactic center region is generally higher than the value of ~15 expected from the "Standard Conversion Factor" (SCF) of 12CO integrated line intensity to H_2 column density. In the 9'-beam, this ratio is in the range from 30 to 200, mostly ~60 to 80. From LVG calculations, we estimate that the large scale 12CO(1-0) emission in the Galactic center region is of moderate (tau >~ 1) or low optical depth (tau < 1). Higher optical depths (tau >= 10) are restricted to very limited regions such as Sgr B2. In addition, we estimate H_2 densities and kinetic temperatures for different ranges of intensity ratios. A considerable amount of molecular mass is in a widespread molecular gas component with low densities and high kinetic temperatures. From our C18O measurements and from results based on dust measurements, the total molecular mass is found to be 3 (+2, -1) 10^7 M_o. We show that the SCF is not valid toward the Galactic bulge. It overestimates the H_2 column density by an order of magnitude because the assumptions required for this factor of optically thick 12CO emission and virialization of the molecular clouds are not fulfilled for a significant fraction of the molecular gas. Therefore, one can also not apply a modified conversion factor to the Galactic center region since the 12CO luminosity is not directly related to the H_2 mass. A comparison with results from bulge regions of external galaxies indicates that the 12CO emission is generally not a suitable tracer of H_2 masses in the central regions of galaxies.