A paper (PDF) by Tom Higham and colleagues presents a redated chronology for the late Neandertals from Vindija, Croatia. There are two directly dated hominid specimens (Vi-207 mandibular fragment and Vi-208 parietal fragment). Earlier work by Smith et al. (1999) had dated the two specimens to between 28,000 and 29,000 BP.
The current paper notes a possible problem with contamination by more recent carbon in the specimens, which would make the dates younger than they ought to be. So Higham et al. (2006) used a new method that filters out small molecules from the collagen extracted from the bone. This resulted in older date estimates, 32,400 +- 800 BP, and 32,400 +- 1800 BP, respectively.
There is a news release describing the work.
The paper also provides a useful short review of the current radiocarbon chronology of late Neandertal and early modern skeletal remains in Europe. This quote is illuminating:
This situation currently makes it difficult to use an archaeological complex, such as the Aurignacian, as a correlate for the spread of modern humans across Europe during this biocultural evolutionary transitional time period (in contrast to Mellars 2005). Several factors play into this ambiguity. It is possible that the dating difficulties described above with reference to Vindija may be more widespread than hitherto anticipated, and that the 4,000-year gap between the earliest directly dated modern humans and the earliest Aurignacian is a function of radiocarbon acccuracy on the few dated specimens...
I pause the quote to point out that the authors earlier note the lack of association with skeletal remains for the early Aurignacian; thus the question is whether the early Aurignacian itself is dated too early. Of course, if the problems with the radiocarbon chronology were of the same type that they found with the Vindija bones (i.e., contamination with young carbon), the other dates wouldn't be too old, they would be too young. So it would have to be some other problem. Maybe all the supposedly old early Aurignacian will turn out to be
The gap may be a function fo the scarcity of Aurignacian human remains and the low number of dated specimens...
Although perhaps one wouldn't expect that all the dated specimens would be archaeologically recent compared to the Aurignacian as a whole...
Alternatively, it may be a result of semiindependence of the spread of the Aurignacian (a cultural process) and the westward dispersal of early modern humans (a biological population process) (Higham et al. 2006:555).
The fact is that we don't currently know. It seems sort of unlikely that the current collection of fossils and sites is adequate to tell us -- if there were skeletal associations with several early Aurignacian sites, that would be one thing, but there just aren't. The current chronology does place Mladec younger than Vindija, so the prior overlap of Neandertal and early modern specimens in central Europe is no longer. It makes it even more suggestive that the Vindija G1 assemblage includes Aurignacian elements.
Higham T, Ramsey CB, Karavanic I, Smith FH, Trinkaus E. 2006. Revised direct radiocarbon dating of the Vindija G1 Upper Paleolithic Neandertals. Proc Nat Acad Sci USA 103:553-557. Abstract
Smith FH, Trinkaus E, Pettitt PB, Karavanic I, Paunovic M. 1999. Direct radiocarbon dates for Vindija G1 and Velika Pecina Late Pleistocene hominid remains. Proc Nat Acad Sci USA 12281-12286. Full text online