As reported by ArsTechnica, there has been a second case of a melting MagSafe connector. Apple's MacBook and MacBook Pro models both use a new charging interface called MagSafe. Consisting of 5 magnetically attached pins (only 4 provide power), MagSafe safely disconnects from the MacBook if the cord is tugged or tripped on. However, one MacBook Pro user reported that his cable started melting while he was using it. The moral of the story? Don't let your MacBook Pro charge unattended. There are no reported cases of this happening on any MacBooks, which use a 60 Watt power adapter where as the MacBook Pros use an 85 Watt adapter. I almost had a MagSafe mishap when a stray USB connector found its way to my MagSafe port and adhered to it. Luckily enough I was able to separate them before it made full contact.
The MagSafe connector is in the back.