Determining the structure-to-property relationship of materials becomes particularly challenging when the material under investigation is dominated by defects and structural disorder. Knowledge on the exact atomic arrangement at the defective structure is required to understand its influence on the functional properties. However, standard diffraction techniques deliver structural information that is averaged over many unit cells. In particular, information about defects and order-disorder phenomena is contained in the coherent diffuse scattering intensity which often is difficult to uniquely interpret. Thus, the examination of the local disorder in materials requires a direct method to study their structure on the atomic level with chemical sensitivity. Using aberration-corrected scanning transmission electron microscopy in combination with atomic-resolution electron energy-loss spectroscopy, we show that the controversial structural arrangement of the Fe2O2+δ layers in the mixed ionic-electronic conducting Sr4Fe6O12+δ perovskite can be unambiguously resolved. Our results provide direct experimental evidence for the presence of a nanomixture of "ordered" and "disordered" domains in an epitaxial Sr4Fe6O12+δ thin film. The most favorable arrangement is the disordered structure and is interpreted as a randomly occurring but well-defined local shift of the Fe-O chains in the Fe2O2+δ layers. By analyzing the electron energy-loss near-edge structure of the different building blocks in the Sr4Fe6O12+δ unit cell we find that the mobile holes in this mixed ionic-electronic conducting oxide are highly localized in the Fe2O2+δ layers, which are responsible for the oxide-ion conductivity. A possible link between disorder and oxygen-ion transport along the Fe2O2+δ layers is proposed by arguing that the disorder can effectively break the oxygen diffusion pathways.