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We describe experimental and theoretical studies of the effects of resonant electronic state coupling on the formation of ultracold ground-state $\mathrm{<mrow\; data-mjx-texclass="ORD">85</mrow>}$Rb$2$. The molecules are formed by photoassociation of ultracold atoms in a MOT into the 0 state converging to the $5S+5P1/2$ limit, followed by radiative decay into high vibrational levels of the ground electronic state, $X 1\Sigma g+$. The populations of these high-$v$ ground-state levels are monitored by resonance-enhanced two-photon ionization (R2PI) through the $2 1\Sigma u+$ state. We find that the populations of vibrational levels $v″$=112-116 are far larger than can be accounted for by the Franck-Condon factors for $0u+\leftarrow X 1\Sigma g+$ transitions. Further, the total number of ground-state molecules formed by this process exhibits oscillatory behavior as the PA laser is tuned through a succession of $0u+$ state vibrational levels. Both of these effects are explained by a new calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling between the two $0u+$ states converging to the $5P1/2$ and $5P3/2$ limits. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules. \vspace{12 pt} We also describe evidence from our R2PI spectra for extensive singlet-triplet mixing between excited states of Rb$2$ at intermediate internuclear separations, apparently also induced by spin-orbit interactions. In particular, the $3 1\Sigma g+$ and $1 1\Delta g$ states converging to $5s+4d$ have been observed in excitation from the $a 3\Sigma u+$ state,}, 261 (2006).} and the $2 3\Pi u$ state has been observed in excitation from the $X 1\Sigma g+$ state.