Dynamic force measurements have been made between an oil drop and a silica particle in surfactant and sucrose solutions with viscosities that range up to 50 times that of water. These conditions provide variations in the shear rate and the relative time scales of droplet deformation and hydrodynamic drainage in a soft matter system. The results obtained indicate that soft deformable boundaries have a natural response that limits the maximum shear rate that can be sustained in thin Films compared to shear rates that can be attained in films bounded by rigid boundaries. In addition, to extend boundary slip studies on rigid surfaces, we use a smooth deformable droplet surface to probe the dependence of the boundary slip on fluid viscosity without the added complications of surface roughness or heterogeneity. Imposing a Navier slip model to characterize possible slip at the deformable oil-sucrose solution interface gives results that are consistent with a slip length of no lamer than 10 inn over the range of solution viscosity studied, although an immobile (zero slip length) condition at the oil-sucrose solution interface is perfectly adequate. In high viscosity solutions, cantilever motion at high scan rates induces a significant cantilever deflection. A method has been developed to account for this effect in order to extract the correct dynamic force between the deformable drop and the particle.