How can I do a screen recording on the S3? I need to record my screen as I'm using a specific app to show the issues showing up that a developer is  unable to replicate.  How can I achieve this? Is screen recording even possible on Android?

OS: 4.1
Most screen recording applications require rooting your phone, unfortunately.

You can try EASY screen recorder NO ROOT (paid version here): it is the most well-rated screen recording application that does not need root I am aware of.

A few other applications: