We investigate the electronic structure of Sr2FeMoO6 combining photoemission spectroscopy with a wide range of photon energies and electronic structure calculations based on first-principle as well as model Hamiltonian approaches to reveal several interesting aspects. We find evidence for unusually strong Coulomb correlation effects both in the Fe 3d and O 2p states, with an enhanced manifestation in the majority spin channel. Additionally, O 2p states exhibit a spin splitting of nonmagnetic origin, which nevertheless is likely to have a subtle influence on the stability of the ferromagnetism of this compound.