There has been recent controversy about the magnitude of spin-flipping in the heavy metal Pt, characterized by the spin-diffusion length, lsf(Pt) We propose a resolution of this controversy, and also present evidence for the importance of a phenomenon neglected in prior studies of transport across sputtered Ferromagnetic/Pt (F/Pt) interfaces, spin-flipping at the interface. The latter is characterized by an interface spin-flipping parameter, delta(Co/Pt) that specifies the probability P = [1 - exp(-delta)] of a conduction electron flipping its spin direction as it traverses a Co/Pt interface. From studies of the Current-Perpendicular-to-Plane (CPP) Resistances and Magnetoresistances of sputtered ferromagnetically coupled Co/Pt multilayers by themselves, and embedded within Py-based Double Exchange-biased Spin-Valves, we derive values at 4.2K of delta(Co/Pt) = 0.9 (+0.5/-0.2), the interface specific resistance, AR*(Co/Pt) = 0.74 +/- 0.15 fohm-m(2). and the interface spin-scattering asymmetry, gamma(Co/Pt) = 0.58 +/- 0.12. This value of delta(Co/Pt) is much larger than ones previously found for interfaces involving Co but not Pt. To derive delta requires knowledge of the spin-diffusion length, lsf(Pt), for our sputtered Pt. We derive lsf(Pt) from separate measurements. Combining our results with those from others, we find that lsf(Pt) for Pt is approximately proportional to the inverse resistivity, 1/rho(Pt).