No audio on the right channel

It is probably some dirt in- or another problem with your sound-output jack.

If twisting your headphone-cable or repeatedly plugging it in and out of your MacBook does not work, you might fix it by doing something like (gently!) poking into it with the backside of a matchstick or trying to clean it with some cotton buds. In that case make sure you have one that does not fall apart easily or you'll end up with a cotton-filled connector.

If that does not work, I'm not sure if you are able to fix it yourself since your MB might need to be taken apart to get into the jack and clean it…

Check your settings in System Preferences > Sound > Output.

I had the same problem and for some mysterious reason my left-right balance was completely screwed up.

No idea how it happened but once I adjusted it to center it now plays back perfectly (:

This is also a long shot, but check under System Preferences -> Universal Access -> Hearing and see if "Play stereo audio as mono" is checked.

One other possibility: plug your headphones in and run Audio MIDI Setup (it's in Applications/Utilities). See if one of the output channels is turned down or muted. Be sure your headphones are plugged in because OS X has separate settings for headphones and built-in speakers and switches between them automatically.