Just to add, IR-modes are not necessarily Raman-inactive except if the molecule or the unit cell has an inversion center as symmetry element. Or, to put it in another way, for centrosymmetric molecules/unit cells some of the Raman-active modes are also IR-active.
That may depend on the surroundings in your system. If something around your molecules interacts strongly, the symmetries and degeneracies may be lowered which may allow activity of otherwise inactive modes. A typical example of this is SERS, check out this example:
Article SERS of gold/C 60 (/C 70) nano-clusters deposited on iron surface
Just to add, IR-modes are not necessarily Raman-inactive except if the molecule or the unit cell has an inversion center as symmetry element. Or, to put it in another way, for centrosymmetric molecules/unit cells some of the Raman-active modes are also IR-active.
As already mentioned, if additional modes are observed, something in your systems (molecule or solid state plus their surroundings) has to deviate from the ideal structure, which was assumed to calculate/identify the number of Raman and IR active modes, e.g. by group theory. Whenever you observing other modes, something has happened, examples are defects or interfaces (both can lower symmetry), strain/stress (lower symmetry), modes may be activated by electronic contributions ("resonant raman") etc.
A good example is the spectrum of graphene. By selection roles, it should only show one single line, yet the Raman spectrum of Graphene is very rich and shows peaks and combination lines activated by defects, a strong spectrum due to resonante enhancements and electronic contributions in the K-valleys, etc.
If you detect otherwise non-allowed peaks, it is usually a change to learn something more about the system.