The latest full sky surveys (globular clusters), along with results of WMAP and the high Z-supernovae data show, within margin of error, that there is no inconsistency with the Age of the Universe, and the oldest stellar structures. Everything seems to be fitting nicely. Historically, this was not the case...but that was due to major errors in dating, going back to the original crisis when there wasn't an understanding of the difference between Population 1 and Population 2 stars.
However, things have been pretty much rosy, at least since the mid to late 1960s. All subsequent data and observations have reinforced the fact that the Universe is older then the oldest observed structures (e.g. stars, galaxies, globular clusters, etc.).