We present in this paper high signal-to-noise long-slit optical spectra of the Extended Red Emission (ERE) in the "Red Rectangle" (RR) nebula. These spectra, obtained at different positions in the nebula, reveal an extremely complex emission pattern on top of the broad ERE continuum. It is well known that three features converge at large distance from the central object, in wavelength and profile to the diffuse interstellar bands (DIBs) at lambda5797, lambda5849.8, and lambda6614 Angstrom (e.g. Sarre et al. 1995). In this paper we give a detailed inventory of all spectral subfeatures observed in the 5550-6850 Angstrom spectral range. Thanks to our high S/N spectra, we propose 5 new features in the RR that can be associated with DIBs. For the 5550-6200 Angstrom spectral range our slit position was on top of the NE spike of the X shaped nebula. A detailed description of the spatial profile-changes is given of the strongest features revealing that even far out in the nebula at 2400 from the central star, there remains a small shift in wavelength of 1 respectively 2 Angstrom between the ERE subfeatures and the DIB wavelengths of lambda5797.11 and lambda5849.78 Angstrom.