I have had this problem for ages but thought that would be sorted out in iOS7. It didn't.
I'm using "manually manage music and videos" in iTunes, and I add music to the phone by drag-amd-drop. I'm positive that each mp3 file contains album art (I'm using Mp3tag to add the art), but when i manually add the files to the iPhone via iTunes the album art is not showing on several of the albums, and on some albums the art is wrong and taken from other files.
If you are using the same method as me when you add music to the iPhone and the album art shows correctly, how do you do it? How do you add cover art to the files? Are there more ways to save album art to mp3s than the way mp3tag is doing it?