Recent studies show that the magnetic properties of epitaxial thin films of magnetite (Fe3O4) deviate strongly from bulk behavior: it is difficult to saturate thin films, ultrathin films may become super paramagnetic, their saturation magnetization drops to zero, and the local magnetic moments are oriented out of plane in zero field. The possible relationship between this anomalous behavior and the occurrence of anti-phase boundaries (APBs) is discussed. Transmission electron microscopy images confirm that APBs are present in our Fe3O4 films grown by molecular beam epitaxy on MgO(100). Only APBs with out-of-plane shift vectors are visible. The much higher APB density found in sputtered films suggests that preparation conditions are important. To explain the deviating saturation and the superparamagnetic behavior of thin Fe3O4 films at the same time, the magnetic coupling over the APB must be dramatically reduced due to spin disorder along the boundaries.