As a candidate ‘super-Chandrasekhar’ or 09dc-like Type Ia supernova (SN Ia), SN 2012dn shares many characteristics with other members of this remarkable class of objects but lacks their extraordinary luminosity. Here, we present and discuss the most comprehensive optical data set of this SN to date, comprised of a densely sampled series of early-time spectra obtained within the Nearby Supernova Factory project, plus photometry and spectroscopy obtained at the VLT about 1 yr after the explosion. The light curves, colour curves, spectral time series and ejecta velocities of SN 2012dn are compared with those of other 09dc-like and normal SNe Ia, the overall variety within the class of 09dc-like SNe Ia is discussed, and new criteria for 09dc-likeness are proposed. Particular attention is directed to additional insight that the late-phase data provide. The nebular spectra show forbidden lines of oxygen and calcium, elements that are usually not seen in late-time spectra of SNe Ia, while the ionisation state of the emitting iron plasma is low, pointing to low ejecta temperatures and high densities. The optical light curves are characterised by an enhanced fading starting ∼60 d after maximum and very low luminosities in the nebular phase, which is most readily explained by unusually early formation of clumpy dust in the ejecta. Taken together, these effects suggest a strongly perturbed ejecta density profile, which might lend support to the idea that 09dc-like characteristics arise from a brief episode of interaction with a hydrogen-deficient envelope during the first hours or days after the explosion.