Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are high-information, coherent observables. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, three-dimensional (3D), photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyze the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed analysis [Hockett, Phys. Rev. Lett. 112, 223001 (2014)10.1103/PhysRevLett.112.223001] concerning the main spectral features, but also indicate unexpected symmetry breaking in certain regions of momentum space, thus revealing additional continuum interferences which cannot otherwise be observed. These observations reflect the presence of additional ionization pathways and, most generally, illustrate the power of maximum-information measurements of coherent observables for quantum metrology of complex systems.