Anyone else having problems downloading to iPlayer since Mavericks upgrade?

Working fine for me here.
Tried a Flash update?
I seem to recall being prompted for a Java update as well.

iPlayer downloader uses Adobe Air. That might need an update, though the application generally bugs you about it if you need it.

There are a number of *cough* unofficial iPlayer downloader apps that work fine and don't require any Adobe-related faffery. Given I've paid for the programmes already, I don't have any great moral quandaries about using them.