I uploaded all of my music to Gplay, about 2500 songs. I went through and organized a lot of them by putting a thumbs down next to the ones I didn't want/listen too/like and then when I was all done I would sort all the thumbs down and mass delete them. I've gotten rid of about 500 songs that way, it was really helpful. I suggest this method for organizing.
Then I restarted my computer one day, and all the songs were re-synced and back on the device, thankfully they all came back under "Recently Added" so I was able to delete them all again. (I fixed this by going into the desktop app and checking don't sync all music) But for anyone that wants to upload to Google Play Music and hasn't yet. I suggest you do all or at least most of your organizing on your PC before uploading. It makes it all the more easier.
And to get back on topic, my album arts are also always wrong and are low res, as well. It honestly doesn't really bother me, but it would be cool if they were all correct. (I can't blame it on Google though because I have the same problem when playing them on my PC)
Update: I know no one is going to read this edit, but.. I installed media monkey a couple weeks ago and that program is awesome, I organized the tags, genres and added correct album art to about 95% of my songs. I then installed Tag-scanner and used that to rename all my files, it does it super quick and easy and makes the song titles look a lot more neat. This process all took me days to do, but its worth it.