While what it does support is cool, what it does not support is more worrying. I doubt the browser will be a high priority for them, so the lack of audio support and web sockets will likely persist for longer than most PC browsers.
Audio in general is still in very infant stages. That is, vendors are experimenting, but unless you're going for "only works in X" there isn't much truly interesting stuff you can do currently, even on PC. I'd love to be corrected on this, mind you. But so far it's either all vendor prefixed from what I can tell, or still rather simple.
As a Wii U owner, I'm actually shocked how great the Wii U's browser is considering how half-baked other parts of the system currently are.
Sure, it doesn't have all of the newest HTML5 features, but compared to your average browser-on-a-console, the Wii U's is surprisingly functional for general purpose web browsing and way better than what I was expecting.
Also, the Hulu, Netflix and Amazon Prime Streaming apps are pretty cool and just beginning to show some of the potential of 'second screen' interaction using the Wii U GamePad. These were actually the killer app for the Wii U for me. I doubt the system will get much third party support, but the video streaming apps are great now and likely to get even better as the "TVii" stuff starts coming online.