50Hz hum from macbook air headphone port

Most of the Macintoshes I've had over the years have had a buzz in the headphone port. It is especially noticeable with low impedance headphones. Some have even had a click when the sound is turned on (i.e. when an alert sound plays, or a song is started in iTunes).

You could try taking it to the Genius bar, they might replace it if it is still under warranty. There could be a short somewhere, or it could just be considered "normal" which is why audiophiles use digital output.

You said the humming stops when you touch the machine, which reminded me of another issue: in some situations, some people can feel a "tingling" sensation when they touch the casing of a portable Mac which is connected to an ungrounded power supply.

So, an idea here: plug the power supply in, but make sure you are using a grounded plug on the power supply. There are some more details in the answers to this question.