I'm also noticing the harshness on the first two tracks. On the first track, it's VERY distorted. I mean distortion is all over everything, the vocals, the bass, the guitars, the drums. It's a creative decision that was made by the band and the producer Dave Fridmann. Listen to the NPR interview and they cop to it. Look up the Sleater Kinney record that Dave Fridmann did, too. It's super-mega blown out. This is kind of his "thing". I went to a music conference once when the Sleater Kinney record came out and Dave Fridmann played some tracks off of it. People were giving him shit, saying that he was ruining records. The thing is, this is how the band wanted these tracks to sound.
On "Inside Out" I don't really hear it as much, but the snare sample is very harsh, almost just white noise. I think maybe that's what you could be reacting to? The rest of the stuff sounds pretty lush to me.
I really like the way that Mike McCarthy's mixes sound on "I Just Don't Understand" and "Let me Be Mine" I hope Spoon does more work with him.