We combine H-1, Li-7, and F-19 NMR methods to selectively investigate polymer, cation, and anion dynamics in polymer electrolytes on various length and time scales and over broad temperature ranges. By mixing unentangled poly(propylene glycol) (PPG) with lithium perchlorate (LiClO4) or lithium bis(trifluoromethylsulfonyl)imide (LiTFSI), fully disordered samples are obtained at all studied concentrations. In static field gradient diffusometry, we observe that the long-range motion of all components slows down when the salt concentration is increased, but the effect is more prominent for PPG-LiClO4 than PPG-LiTFSI electrolytes and, in general, differs for the respective components. The self-diffusion coefficients D of polymer and ions have essentially temperature-independent ratios, where cations are less mobile than anions and do not show Arrhenius temperature dependence. To ascertain short-range motions in broad dynamic ranges, spinlattice relaxation studies, including field-cycling relaxometry, are combined with stimulated-echo experiments. We show that rate and heterogeneity of local lithium and polymer dynamics depend on the salt content. For intermediate salt concentrations, the segmental motion even exhibits bimodal distributions of correlation times tau, implying structures with salt-rich and salt-depleted regions. Relating diffusion coefficients D and correlation times tau, we find that the lithium ion transport is strongly coupled to polymer segmental motion even in polymer electrolytes with micro-heterogeneous salt distributions. Finally, field-cycling susceptibilities reveal that Rouse dynamics is important not only for the reorganization of polymer chains but also for the transport of lithium ions.