The UI is what I'm most hesitant about, in my experience Sony are not great at UI design although I really liked the XMB and was sorry it disappeared on the Vita.
However, what they've shown of multiplayer looks great and for me, the rest of the UI is about getting from what I'm doing now, to what I want to do next. If they remove most of the insane delays, like the time taken to start the PSN store, then download updates and populate the updates onscreen, I'll be happy. Probably I'm really hoping this kind of stuff happens at night, so that when I go in, it's all up-to-date.
Yes, they need to fix the lag (like the current PS Store) while navigating screens.
Sony was frustrating to watch because they kept restarting from zero. Glad to see they at least inherit a little from XMB in PS4. I think people appreciate some continuity from last gen goodness.
Will see how they apply WebKit to deliver an interesting experience. By right, it should mean we can access our PS4 XMB on a PC/Mac also.