Sorry. No TiVo functionality.
I also wonder if Apple can out-TiVo TiVo. I have gotten used to the TiVo recording suggestions [...]
Sorry, but it's doubtful that Apple has any interest in letting us record our own copies of anything. Apple wants us to rent or buy content from the iTunes Store, and that shouldn't change after they ship a TV set of their own.
So how will we watch live events like sports and news? How will we watch the latest episode of a show while it "airs"? By watching live streams from Apple's servers. The same way we watch live streams of Apple keynotes. Been there, done that.
What about pause / rewind / slow-mo of live events? Easy. The Apple television could buffer some or all of whatever you're watching. If you rewind, you're just skipping back in your own local copy. And if you tune into a show in the middle and want to start from the beginning, Apple could reset your stream to start from the beginning from their remote copy.
Apple TV 2.0, as it stands now, uses essentially the same circuit board as iPhone, iPad, and iPod touch. It's cheap, small, and it would be trivial to put it in an HDTV enclosure.
The real key to innovative disruption in the TV industry is controlling it all. How will we control the Apple TV? How will Apple make TV compelling, easy, and cool? With Siri.
You: "Siri, show me all the scoring in this year's Superbowl game."
Siri: "There were seven touchdowns and two field goals. And one two-point conversion. Here's the first touchdown..."
You: "Siri, find any episodes of Star Trek: The Next Generation featuring Ashley Judd."
Siri: "Ashley Judd appeared in these two episodes of Star Trek: The Next Generation. Do you want me to play one of them now?"
You: "Siri, who was that French movie director in Close Encounters?"
Siri: "Francois Truffaut. Would you like to see the movies he directed?"
See how easy things could be? No channel numbers to punch in, no 50-key remotes. No need to record anything. And Siri would make extremely easy to find content. And Siri would make it nearly impossible for anyone else to imitate the Apple TV set. Think about it.