In the Denisova hubbub last month ("Denisova genome FAQ") I didn't hear anyone talking about the FOXP2 sequence of the Denisovans. I can't swear that the paper and supplement  don't discuss the gene somewhere, but a full text search doesn't yield any results. Since Neandertals and living people share the same two unique substitutions, we would probably expect the Denisova sequence to share them also. If not, it would suggest some interesting evolutionary dynamics in Eurasia at the time the Denisovans and Neandertals existed there.
I haven't had a chance to look at the data until now, so I just pulled up the Denisova reads in the genome browser. Humans differ from most primates in FOXP2 at two nonsynonymous substitutions in exon 7 of the gene. For both of these sites, the Denisova sequence is identical to humans and Neandertals, and different from other primates.
There's nothing too newsworthy about that observation, if we follow the assumption that Neandertals and humans share the derived FOXP2 sequence by descent from a Middle Pleistocene common ancestor. Reich and colleagues interpret the sequence similarities of the Denisova and Neandertal sequences as evidence that these two groups stem from a more recent common ancestral population than either shared with Africans.
The alternative explanation, that one or both substitutions had occurred recently in humans and introgressed into Neandertals (or vice versa) was based on the significant evidence for reduced variation around the FOXP2 gene, consistent with a recent selective sweep. Coop and colleagues  confirmed that selection was likely recent, but Ptak and colleagues  later demonstrated that the FOXP2 substitutions were probably not the target of recent selection, because the linkage across them was not indicative of a complete sweep. Without evidence for a recent sweep, we cannot give a date for the occurrence of either substitution.
Finding the human-specific substitutions in the Denisova sequence helps to narrow down the evolution of language in the human lineage. If both substitutions were present in the ancestors of the Neandertal-Denisova-African trichotomy, any selection associated with these substitutions must have occurred prior to the divergence of these hominins. By the timeline of Reich and colleagues , that would be prior to 250,000-400,000 years ago. Remembering that we do not really know the function of these substitutions, it suggests at least a novel adaptive environment for communication in humans during the early to mid-Middle Pleistocene. Given the evidence of humanlike hyoid and middle ear morphology at Sima de los Huesos, this Middle Pleistocene development of human communication ability may also be unsurprising.
- Genetic history of an archaic hominin group from Denisova Cave in Siberia. Nature [Internet]. 2010;468:1053–1060. Available from: http://dx.doi.org/10.1038/nature09710
- . The Timing of Selection at the Human FOXP2 Gene. Molecular Biology and Evolution [Internet]. 2008;25:1257–1259. Available from: http://dx.doi.org/10.1093/molbev/msn091
- . Linkage Disequilibrium Extends Across Putative Selected Sites in FOXP2. Molecular Biology and Evolution [Internet]. 2009;26:2181–2184. Available from: http://dx.doi.org/10.1093/molbev/msp143