I just posted this in another thread:
It appears there may be (or have been) two similar, but not necessarily related, issues:
1) Plugging or unplugging via USB could (would?) clear whatever was in Now Playing in the Music app, causing the first song in your library to start playing. This was an issue in some cases (playing from Artist view) but not others (playing a playlist). Since 7.1 this hasn't been an issue for me.
2) When playing audio/video in another app (I've verified with Safari and Chrome; not sure about others), that app never gets cleared out of the global player, even after it is done playing and/or the app is closed. For an example, if you play a YouTube video in Chrome, then close the page and quit Chrome, "Chrome" is still displayed in the global player in the Control Center. Hitting play there won't do anything. However, it seems that when you plug in via USB, it really wants to start playing *something*, so it starts playing the start of your library. What's interesting, though, is that until you do so, Now Playing in the Music app isn't affected. That is, while the Control Center will just say "Chrome", Now Playing in the music app will show whatever had been playing before, and if you press play there before plugging in again via USB, playback will resume where it should. It seems like in theory this could affect playback other than USB, but so far, in my experience, trying to play via Bluetooth or hitting play (either in the Control Center or via the headphone remote) doesn't result in anything happening. That is, playback doesn't actually start.