This work aims at theoretical consideration of weak effects, some of which are well-known in molecular spectroscopy, and some are not yet fully elaborated. A cohesive element of our consideration consists in the use of the original perturbative approach, which significantly facilitates the derivation of the sought expressions and their employment for applications. We consider several examples of perturbative problems concerning permitted or forbidden electric dipole and permitted magnetic-dipole transitions. The suggested approach can be generalized to other effects involving electronic, spin, and higher-order perturbations in molecular spectra.