Just listened to all the songs a few times, and here are my initial impressions. I seemed to like every song more with each additional listen; after I threw out my notions of what the
original songs sounded like.
Here's a rundown of my favorite cuts:
Though I'm hugely biased (I've long loved Marianne) I still think Marianne Faithfull's rendition of Angel is my favorite track of the album. And I don't even like Fleetwood Mac's version of Angel!

To me, she captures the essence that the original was going for, but could not. Marianne's is simpler, folksier, and wonder of wonders, it actually has a climax at the end! The Fleetwood Mac original just wandered aimlessly & never went anywhere in my opinion.
I thought it was really cute & cheeky what Gardens & Villas did with Gypsy. I would have
never picked out the very Asian melody running throughout Gypsy, but these folks did & brought it to the surface.
Craig Wedren and St. Vincent's version of Sisters was appropriately spooky and rocking. I thought it would have benefitted from a single singer, though.
I very much liked the spacey yet literal take on Straight Back.
Same with Green Manalishi. The Entrance Band's version is sort of a more elaborate version of the original... on acid.

I can't stop listening to it. I didn't think a whole lot of it until I really cranked the volume & let the vocals, bass, and drums hit hard (those are the best parts of the original, IMO). This probably ties as my other favorite on the album.
HAIM's version of Hold Me is just pure fun.
Tame Impala's version of That's All For Everyone is pretty cool. This is probably the sound Lindsey was going for originally, but somehow didn't attain. The ending goes on way too long, though.
Honestly, the rest of the album falls pretty flat for me, though:
The autotuned robot vocals on MGMT's version of Future Games utterly ruined that song for me (I *HATE* that effect with a passion. It's the dumbest production "trick" in the book).
I've heard Landslide far too many times to like any rendition of it anymore.
Rhiannon was a pure hipster farce.
Billy Gibbons' version of Oh Well is exactly what you'd expect it to sound like (not that this Texan doesn't adore ZZ Top). Yawn.
I really like The New Pornographers version of Think About Me, sans the harmonies... they're very amateurish.
Lykki Li's version of Silver Springs was fine until I realized the song would not ramp up & take off like the original. Silver Springs IS the crescendo that the song builds up to.
Karen Elson's Gold Dust Woman is predictable, even though I know not who she is. Some of the production elements are fantastic, others are not.
Storms would have been fine sans for the insincere vocals/harmonies. The original is so raw & emotive. These guys just sound like they're going through the emotions here. And everything after the vocals stop at the end of the song is just filler noise. I do like the rain at the end, though.
The Kills version of Dreams reminds me of Bekka Bramlett covering Stevie's songs with the Mac during the Time Tour. Great voice, but wrong singer to be covering Stevie Nicks... the whole thing just comes across trashy.
The cover of Tusk is interesting until you realize it doesn't have a climax. Mick's crazy drum solo is what makes that song.