Phonon frequency and linewidth as well as quasielastic scattering due to spin energy fluctuations are used to evaluate the evolution of spin correlations in a spin chain system with considerable interchain coupling. In the compound CuSe2O5 these interactions lead to long-range order and a regime with enhanced classical critical dynamics. The resulting anomalies include the observation of quasielastic scattering intensity in interchain polarization, in addition to the usually reported intrachain polarization as well as the persistence of fluctuations to temperatures down below T-N. The inverse of the spin correlation length shows a linear temperature dependence with an offset at T-N. Finally, the derived magnetic contributions to the specific heat are pronounced around T-N while contributions due to one-dimensional fluctuations are hardly visible.