Atoms in a rod of iron has discrete energy levels. When we heat it, its electrons after absorbing photons rise to next energy levels and then fall back emitting radiations. As all iron atoms are alike so radiations of same wavelength should be given off by iron atoms. Am I missing something?
Iron atoms, as a dilute gas, have discrete energy levels. An iron rod, however, has broad energy bands instead, has oxides and other scale compounds on its surface, and at high temperatures, even Doppler shifts and internal vibrations can significantly wash out the atomic spectrum features.
Impurities also give rise to extra energy levels.
One can expect a few gaps, but many features of the blackbody curve will show up in the hot-solid-iron spectrum. All the 'lines' of iron, all the hybridized orbitals that bond the metal together (bands), all the spreading of those lines due to pressure, shifts due to fields, and just plain randomness of temperature, work against a sharp spectral-lines result.