I've never really been fully on board with the Flaming Lips (maybe in part because I've never managed to catch one of their famously great live shows) - Transmissions is mostly good and occasionally great, Soft Bulletin is very good but hardly a classic, Yoshimi has its moments but ultimately I think it's too messy to amount to anything much as a whole, and that's about as far as I've got with the band, albums-wise.
Still, they do have the ability to produce some pretty great moments, and I was hopeful that At War With The Mystics might have at least a handful of those...opener "The Yeah Yeah Yeah Song" annoys me a bit - though it seems to've been picked up by the radio - but the next couple, the sharp-edged/catchy "Free Radicals" and the disco-turns-to-prog "The Sound of Failure/It's Dark...Is It Always This Dark??" are cool, and things go along pretty well thereafter ("Mr Ambulance Driver" makes a lot more sense in the context of the album), wandering similar byways to those trodden in their last couple of albums (airy keyboards, crashing percussion, quasi/actually epic verses, etc), though maybe with a bit more emphasis on the guitar heroics, Lips-style...
It seems like a denser album than Yoshimi or Soft Bulletin, and there are a fair number of resonances between songs - shared or similar chord progressions and so on...all up, in keeping with that complexity/ambition, it's quite proggy, right down to the occasionally epic song lengths and progressions ("The Wizard Turns On..." in particular, while relatively short, could've come right off a record like Piper at the Gates of Dawn, and not just because of its title); also, it's a bit more chaotic and in that respect more in lie with their earlier stuff (though with the latter-day glossiness). I'll need to live with it for a while longer before coming to a final conclusion (I've already had it for a few weeks, maybe a whole month, but not listened to it that much) but it seems pretty good.