If you've seen Karate live, especially in post 2000 shows, you'll have noticed that there seems to be a lot of improvization happening, even occasionally drifting into avant-garde. On several occasions, I have confronted them with this point after shows, and have found that all of these "improv" sections are actually all planned out, like a Rush concert.
I would assume the same for "Unsolved" on which almost every song has some sort of jazzy guitar solo by Geoff Farina. But bear in mind that this is not a new direction for Karate, it has simply been exploited far more on this album.
Generally, the songs are slower, some of them swing, there are a couple of true rockers ("Sever" is as impressive on album as it is live) but all in all less yelling and a more conversational tone to the lyrics. Confusingly, there are also some delay/feedback Thurston Moorish soundcapes in many of these songs, which are often coupled with some fancy drum work. And speaking of fancy drum work, check out the tension/release coda of the album, the 15 minute "This Day Next Year" which next to "Diazapam" from The Bed Is In The Ocean is one of my favorite Karate songs.
One last thing: The sounds on this album are all crisper than crisp, which goes against the scratchy indie-rock aesthetic. Another rumor I heard was that G. Farina, unsatisfied with his guitar sound both live and in studio, took some time off from recording and touring to study the mechanics and electronics of amplifiers, so that he could better fine-tune his sound. The result: Unsolved is perhaps the best mixed album I have ever heard, though some might hear it and claim it adds to this albums supposed wimpyness. Well, this album has its dull moments, but all and all it is an enthralling album.