The selenium isotopes lie at the heart of a tumultuous region of the nuclear chart where shape coexistence effects grapple with neutron-proton pairing correlations, triaxiality, and the impending proton drip line. In this work, a study of 72Se by internal conversion electron and γ-ray spectroscopy was undertaken with the SPICE and TIGRESS arrays. New measurements of the branching ratio and lifetime of the 02+ state were performed, yielding a determination of ρ2(E0;02+→01+)=29(3) milliunits. Two-state mixing calculations were performed that highlighted the importance of interpretation of such E0 strength values in the context of shape coexistence.