I just installed the Chromecast app on my iPad (2). The iPad is running 6.1.3 (or whatever; it says it's up-to-date).
I've also got a Chromecast that works fine from my Android phone, my Nexus 7 tablet, and all the computers in my house that I've tried (except Linux machines of course).
The Chromecast app tries to find local devices, but apparently it cannot find mine. I've only got one domain in my house, and everything's on the same one. Neither the iPad app nor the Chromecast itself seem to offer any clear way to figure out what's wrong.
So: is there something dumb I'm missing? Unfortunately I don't have any other iOS devices from which to try this. The iPad is otherwise unremarkable and seems to be able to do anything else it's asked to do.
edit — for what it's worth, I also can't get either YouTube or Netflix (the apps) to think that the Chromecast exists.