The polymer dynamics in concentrated solutions of poly(N-isopropyl acrylamide) (PNIPAM) in D2O/CD3OD mixtures is investigated in the one-phase region. Two polymer concentrations (9 and 25 wt%) and CD3OD contents in the solvent mixture of 0, 10 and 15 vol% are chosen. Temperature-resolved dynamic light scattering (DLS) reveals the collective dynamics. Two modes are observed, namely the fast relaxation of polymer segments within the blobs and the slow collective relaxation of the blobs. As the cloud point is approached, the correlation length related to the fast mode increases with CD3OD content. It features critical scaling behavior, which is consistent with mean-field behavior for the 9 wt% PNIPAM solution in pure D2O and with 3D Ising behavior for all other solutions. While the slow mode is not very strong in the 9 wt% PNIPAM solution in pure D2O, it is significantly more prominent as CD3OD is added and at all CD3OD contents in the 25 wt% solution, which may be attributed to enhanced interaction between the polymers. Neutron spin-echo spectroscopy (NSE) reveals a decay in the intermediate structure factor which indicates a diffusive process. For the polymer concentration of 9 wt%, the diffusion coefficients from NSE are similar to the ones from the fast relaxation observed in DLS. In contrast, they are significantly lower for the solutions having a polymer concentration of 25 wt%, which is attributed to the influence of the dominant large-scale dynamic heterogeneities. To summarize, addition of cosolvent leads to enhanced large-scale heterogeneities, which are reflected in the dynamic behavior at small length scales.