Raman scattering spectra of new Fe-based S=2 spin ladder compound BaFe$_2$Se$_2$O are measured in a temperature range between 15 K and 623 K. All six A$_{1g}$ and two B$_{1g}$ Raman active modes of BaFe$_2$Se$_2$O, predicted by the factor-group analysis, have been experimentally observed at energies that are in a rather good agreement with the lattice dynamics calculation. The antiferromagnetic long-range spin ordering in BaFe$_2$Se$_2$O below $T_N$=240 K leaves a fingerprint both in the A$_{1g}$ and B$_{1g}$ phonon mode linewidth and energy. In the energy range between 400 and 650 cm$^{-1}$ we have observed magnetic excitation related structure in the form of magnon continuum, with the peaks corresponding to the singularities in the one dimensional density of magnon states. The onset value of magnetic continuum (2$Δ_{S}$) is found at about 437 cm$^{-1}$ at 15 K. The magnetic continuum disappears at about 623 K, which lead us to conclude that the short-range magnetic ordering in BaFe$_2$Se$_2$O exists apparently up to 2.6$T_N$.