Indistinguishable photons play a key role in quantum optical information technologies. We characterize the output of an ultra-bright photon-pair source using multi-particle tomography [R. B. A. Adamson et al., Phys. Rev. Lett. 98, 043601 (2007)] and separately identify coherent errors, decoherence, and distinguishability. We demonstrate generation of high-quality indistinguishable pairs and polarization NOON states with 99% fidelity to an ideal NOON state. Using a NOON state we perform a super-resolving angular measurement with 90% visibility.