I thought Shenanigans was a studio album? International Superhits was the compilation + 2 unreleased tracks, I think Shenanigans was new material. I'm actually just listening to it again now, and it's not too bad. Listening to it helps me console the gap between the sound on American Idiot and the sound pre-Warning. At least their sound changes over time.
I think everyone agrees on Nimrod though, easily the best album. Kind of funny, in that it had just gotten into them when Nimrod came out, and each of the eagerly anticipated albums I bought after that were let down's compared. Actually, screw Shenanigans, it's gotten boring, I'm listening to Nimrod again!
The latest Weezer and Green Day both have redeeming qualities that make them worth being alive for, and if they were dead, I'm pretty sure I'd be sick of them being idolized all the time. Billy Joe, Rivers, I'm glad you're both still alive.
I don't know if you're familiar with Ben Kweller, but his album "Sha Sha" is very much influenced by weezer. I've actually had people ask me if it's the post-blue pre-green stuff I keep going on about. You can tell it's a different writer after a listening to the songs, but it's good stuff.