We investigate electronic transport in epitaxial Fe(100)/MgO/Fe/MgO/Fe double magnetic tunnel junctions with soft barrier breakdown (hot spots). Specificity of these junctions is continuous middle layer and nitrogen doping of the MgO barriers which provides soft breakdown at biases about 0.5 V. In the junctions with hot spots we observe quasiperiodic changes in the resistance as a function of bias voltage which point out formation of quantum well states in the middle Fe continuous free layer. The room-temperature oscillations have been observed in both parallel and antiparallel magnetic configurations and for both bias polarizations. A simple model of tunneling through hot spots in the double barrier magnetic junction is proposed to qualitatively explain this effect.