The quercetin molecule is known to be an effective pharmaceutical compound of a plant origin. Its chemical structure represents two aromatic A and B rings linked through the C ring containing oxygen and five OH hydroxyl groups attached to the 3, 3′, 4′, 5, and 7 positions. In this study, a novel conformational mobility of the quercetin molecule was explored due to the turnings of the O3′H and O4′H hydroxyl groups, belonging to the B ring, around the exocyclic C-O bonds. It was established that the presence of only three degrees of freedom of the conformational mobility of the O3′H and O4′H hydroxyl groups is connected with their concerted behavior, which is controlled by the non-planar (in the case of the interconverting planar conformers) or locally non-planar (in other cases) TSsO3′H/O4′H transition states, in which O3′H and O4′H hydroxyl groups are oriented by the hydrogen atoms towards each other. We also explored the number of the physico-chemical and electron-topological characteristics of all intramolecular-specific contacts—hydrogen bonds and attractive van der Waals contacts at the conformers and also at the transition states. Long-terms perspectives for the investigations of the structural bases of the biological activity of this legendary molecule have been shortly described.