No sooner did we figure out Google added support for private YouTube videos to the Chromecast, than live videos started working as well. We've been checking around and it looks like almost every live stream is working on the Chromecast, but only from a desktop web browser right now. The Android app still reports an incompatibility with live streams.
Upgrading to a new version of Android is always nice, but Nexus users (and just lately, Google Play Edition users) tend to become unwitting beta testers for a lot of apps. Case in point: MLB At Bat, the official news, scores, and video app for Major League Baseball's online subscription service. It didn't work for Android 4.3 users ever since the new version of Android launched in July, but according to the latest changelog, the updated app should be streaming video to everyone now.