Why do we say "approximation" in the dipole approximation in spectroscopy?
As per your linked reference, it's an approximation because only the first term in the expansion (here, unity) is considered.

The issue with transitions that are allowed or forbidden arises as a result of using such an approximation: "Forbidden" transitions are not strictly forbidden, it's just that they are weak and, in the linear approximation of the transition dipole operator, are usually not observed.