I've noticed this several times when playing.

Sometimes a song will begin playing, but when the game is normally supposed to stop it and play another piece of music (such as doing leves or riding a chocobo), the other song will continue playing on top of the other music. Even when switching to another area, it will continue playing. The only quick fix is for me to log out and back in.

Another glitch happened while crafting. It got to a point where my synth was becoming unstable, and of course it makes the sparking/sizzling sound effect. But after the synth returned to normal, it was still making the sound, and even when I was finished, the sound continued. Again, I had to log out and back in to get it to stop.