That's been there since 2.0 I think, but it's not real push. It's some bastardized version...but now in 3.0 (like you've got) it's supposed to be real push.
Battery life is what they need to work on, or give us a bigger capacity battery somehow. With Fetch every 1 hour, 3g turned off, I get MAYBE 12 hours until it goes to 20% warning. Main thing I use this for is email, texting, and some calls. And yet I always have to worry about having a charger with me. RIDICULOUS. American technology is still crap, so is AT&T. Yes, I regret switching from Verizon to AT&T but dealing with it.
Just a rumor but maybe around 2010, iPhone will be available for Verizon. It definitely won't be 09 because of the promotion contract between Apple and AT&T.