The UW-Penning trap mass spectrometer (UW-PTMS) is now able to generate measurements with uncertainties near 10 ppt, making it necessary to address several major systematics, both experimentally and theoretically, in order to improve our present accuracy. These effects range from the image charge shift, originally investigated two decades ago, to the recently investigated limits due to residual magnetron energy. Using the knowledge gained from these studies, the atomic mass of O16 has been completely reviewed and the results of this re-analysis are presented. There is also an adjustment given for the atomic mass of He4 and we present a preliminary result for the atomic mass of H2. In addition, we present our plans for replacing the present spectrometer with a new one containing a cylindrical storage trap that will be loaded using an external ion source and two hyperbolic traps whose dimensions are identical to the Penning trap in our present spectrometer. Thus, it is expected that the new spectrometer will have essentially the same systematics as those described in this paper.