Superconducting (SC) and non-superconducting (non-SC) RbxFe2-ySe2 crystals were grown using the "self-flux" technique in order to assign the rnicrostructural changes to the onset of superconductivity in complex iron selenides. The crystals were thoroughly characterized by magnetic susceptibility and transport measurements as well as powder X-ray diffraction. Special attention was paid to the comparison of the microstructure of the crystals with and without the superconducting transition by means of transmission electron microscopy (TEM). It is shown that the alternation of ordered and disordered regions on the sample surface and along the c-axis is characteristic for both SC and non-SC materials and therefore does not necessarily represent a trigger of superconductivity. Three types of electron diffraction patterns were found for the superconducting RbxFe2-ySe2 sample, of which one is observed for the first time and originates from alkali metal ordering. Moreover, for the superconducting RbxFe2-ySe2 material a monoclinic distortion with beta similar to 87 degrees was observed, leading to the space group I2/m. This monoclinic distortion seems to be an attribute of the superconducting material only, whereas in the non-superconducting sample the orthogonality of the crystallographic axes is preserved.