  Inelastic neutron scattering measurements on the molecular dimer-Mott
insulator $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl reveal a phonon anomaly in
a wide temperature range. Starting from $T_{\rm ins}\sim50$-$60$ K where the
charge gap opens, the low-lying optical phonon modes become overdamped upon
cooling towards the antiferromagnetic ordering temperature $T_\mathrm{N} = 27$
K, where also a ferroelectric ordering at $T_{\rm FE} \approx T_{\rm N}$
occurs. Conversely, the phonon damping becomes small again when spins and
charges are ordered below $T_\mathrm{N}$, while no change of the lattice
symmetry is observed across $T_\mathrm{N}$ in neutron diffraction measurements.
We assign the phonon anomalies to structural fluctuations coupled to charge and
spin degrees of freedom in the BEDT-TTF molecules.
