Mesoscale structural dynamics and rheology of semidilute aqueous dispersions of poly(ethylene oxide) (PEO) containing nanosized silica particles are investigated using mechanical rheometry, optical polarimetry, and dynamic light scattering measurements. The average diameter of silica particles in the dispersions is chosen to be much smaller than the polymer coil diameter to study the effect of polymer-particle interactions on solution properties. For particle volume fractions as low as 0.2%, a nearly 2-fold increase in the solution viscosity and optical anisotropy is observed. At a particle volume fraction of 2% the viscosity and optical birefringence are an order of magnitude larger than in the neat polymer solutions. At low shear rates, polymer-nanoparticle dispersions manifest larger stress-optical ratios than the neat polymer solutions; they violate the stress-optical rule at high shear rates. Nanoparticles are also found to dramatically slow down stress relaxation of the solutions and to shift the onset of shear thinning behavior to lower shear rates. These findings are discussed in terms of the polymer bridging effect, which produces soft colloidal structures that are larger in size than either the polymer or primary particles. Slower dynamics of these secondary structures and flow-induced changes of their shape are argued to produce other properties observed.