We report on the structural and spectroscopic characterization of the multiferroic Fe$_2$Mo$_3$O$_8$. Synchrotron x-ray and neutron diffraction, as well as thermal expansion measurements reveal a lattice anomaly at $T_{mathrm{N}}simeq 60,$K but do not show any symmetry lowering in the magnetically ordered state. The lattice parameter $c$ exhibits a non-monotonic behavior with a pronounced minimum around $200,$K, which is also reflected in an anomalous behavior of some of the observed infrared-active optical excitations and parallels the onset of short-range magnetic order. The infrared reflectivity spectra measured between 5 and 300$,$K in the frequency range of $100-8000,$cm$^{-1}$ reveal most of the expected phonon modes in comparison with the eigenfrequencies obtained by density-functional calculations. The $A_1$ phonons show an overall hardening upon cooling, whereas a non-monotonic behavior is observed for some of the $E_1$ modes. These modes also show a strongly increased phonon lifetime below $T_mathrm{N}$, which we associate with the quenched direction of the orbital moment in the magnetically ordered state. A similar increase is observed in the lifetime of the higher-lying $d$-$d$ excitations of the tetrahedral Fe$^{2+}$ site, which become clearly visible below $T_mathrm{N}$ only.
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