Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the Sr$_2$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. Sr$_2$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr cite{Zelevinsky2008}. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.
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