So my iPhone SE was displaying the wrong album art for a number (though not all) songs. When I checked these albums on iTunes, all the songs had the correct album art. I tried deleting all the songs and then resyncing the playlist, but that didn’t fix the problem. A quick web search turned up the following tip from Reddit.

First delete the playlist, but before starting another sync from the computer, also turn off wi-fi and cellular communications. The easiest way to do this is to place the phone in Airplane mode. Then start the sync, and the correct album art should appear on the iPhone. Apparently this happens when syncing playlists.

What an annoying bug.