@Alex Rusnak: This issue has been resolved in the new 1.1.2 launcher.
For the time being, if you are having this issue, the only workaround is to login while connected to the internet, then after the login, you may turn off the connection once the game screen appears. You will still be able to switch worlds in singleplayer mode, as normal. Make sure that you don't incidentally close the game or you'll have to go through the above process again (which isn't all that grueling).
For now, hang in there until the devs get around to fixing it when they have the time.
Confirmed. Issue persists in 1.7.2. Background music looping appears to be fixed and is no longer an issue, but duplicate chest sounds still persist.