We present high-resolution two-color photoassociation spectroscopy of Bose-Einstein condensates of ytterbium atoms. The use of narrow Raman resonances and careful examination of systematic shifts enabled us to measure 13 bound-state energies for three isotopologues of the ground-state ytterbium molecule with standard uncertainties of the order of 500 Hz. The atomic interactions are modeled using an ab initio based mass-scaled Born-Oppenheimer potential whose long-range van der Waals parameters and total WKB phase are fitted to experimental data. We find that the quality of the fit of this model, of about 112.9 kHz (rms) can be significantly improved by adding the recently calculated beyond-Born-Oppenheimer (BBO) adiabatic corrections [J. J. Lutz and J. M. Hutson, J. Mol. Spectrosc. 330, 43 (2016)10.1016/j.jms.2016.08.007] and by partially treating the nonadiabatic effects using distance-dependent reduced masses. Our BBO interaction model represents the experimental data to within about 30.2 kHz on average, which is 3.7 times better than the "reference" Born-Oppenheimer model. We calculate the s-wave scattering lengths for bosonic isotopic pairs of ytterbium atoms with error bars over two orders of magnitude smaller than previous determinations. For example, the s-wave scattering length for Yb174 is +5.55812(50) nm.