There is an easy way to resolve this issue without having to connect to iTunes and re sync anything. The issue is caused by syncing music to your device that was purchased from multiple Apple ID's. I had music synced on my iPhone from my iTunes library that was purchased under 3 different accounts; my current Apple ID, an old Apple ID and a few songs purchased by my wife from her Apple ID. It seems the issue is a result of iTunes, for some reason, not being able to copy the album art over to your device for songs purchased under a different Apple ID so it oddly just substitutes album art from music you've imported to your iTunes library or album art from albums you've purchased under the Apple ID your currently signed in under. This is the easiest way to resolve the issue right from your device running iOS 10 or later(and possibly some older versions) without having to connect to iTunes:
1. Find an album/song displaying the incorrect album art.
2. Force touch the album cover in your music list or locate the 3 dots icon and tap "Remove" and then "Remove Download/s"(if only "Delete from Library" is available you can tap that too, but in this case you may have to open iTunes on your Mac/PC and "unhide" that item later to redownload it).
3. Launch the iTunes app on your device and navigate to the "More" tab, then "Purchased", then "Music".
4. Find the album/song you just removed from your device and tap the download button(the cloud with the downward arrow).
Once the album/song has finished downloading it should now have the correct album art(It may take a couple minutes for the album art to update. If the incorrect album art persists you'll need to do it again and select the "Delete from Library" option in which case the album/song is likely "hidden" in your "iTunes in the cloud" settings in iTunes. You'll have to "unhide" these albums/songs before you can redownload them.
Additional tip: In order to gain access to music purchased from old accounts on the fly without having to constantly be switching Apple ID's back and forth, enable family sharing and make your new(or main) account the organizer and any other or older accounts family members. This way you can launch the iTunes app on your device and navigate to the "purchased" section where you'll now see additional options for accessing you purchases under those old accounts without having to switch Apple ID's. I've been using this nice little life hack for a couple years and it's extremely convenient.
Hope this helps.