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.
Interesting that it is no longer Opera, but WebKit under the hood according to http://en.wikipedia.org/wiki/Wii_U_Internet_Browser
If as he describes "the data is wiped when the browser is closed", then i think Wii U implemented "SessionStorage".