Can dolphins actually communicate linguistically?
Dolphins and orcas do have dialects. Of course there are species specific dialects and it has been shown that orcas reared with bottlenose dolphins tend to learn the latter's dialect. Dolphins of the same species also seem to have regional dialects, as mentioned in this BBC post (I personally do not trust in non-research articles much, but nonetheless in this case the article indicates a certain possibility of a phenomenon). However, this page also reports the same finding and this source seems to be much more reliable. There are citations too that are at present inaccessible to me. Both the sources say that bottlenose dolphins from Shannon estuary in Ireland, "speak" different dialect compared to those from Cardigan Bay in Wales.

The actual research work is this:


  Hickey, R. (2005) Comparison of whistle repertoire and characteristics between Cardigan Bay and the Shannon estuary
  populations of Bottlenose dolphins (Tursiops truncatus) with
  implications for passive and active survey techniques. School of
  Biological Sciences, University of Wales, Bangor




Apart from having regional dialects, the cetacean communication also seems to have other features of a "language". I am pasting excerpts from this article which basically reports a study on the acoustic communication or codas in sperm whales. This may apply to dolphins as well.


  Individuals within social units have preferred associates among
  members (Gero et al. 2008), indicating differences in the way an
  individual interacts with other members of its unit. These preferred
  associations among unit members suggest the possibility of an
  individual discrimination system.





  .... most adult animals within a social unit shared the most common coda
  types, with the exception of the mother-calf pair whose repertoires
  were different from those of other unit members and each other. Apart
  from the mother-calf differences, the repertoire similarities of other
  members did not support the hypothesis of individually distinctive
  coda type repertoires. This sharing of coda repertoires suggests that
  they allow group membership recognition, at either the unit or clan
  levels. This hypothesis is further supported by the fact that social
  units seem to form groups preferentially with other units of their own
  clan (Rendell &amp; Whitehead 2003b).