I think you may just have either a defective unit or battery. I just got my S3 last week (coming from the original Galaxy Note) and the battery life on it is awesome! I easily get a full days use out of the battery (I keep my brightness level at 50% if you're wondering).
I also bought a battery charger which came with an additional battery. The battery that came with the charger is kind of wonky though. Its a standard OEM battery but when I pop it into the phone it will immediately drop down to 88% within a 10-15 minute period. It will then sit at 88% for an hour or two and then from there the battery percentage readings are normal. But even the spare battery with all of its crazy percentage readings gives me identical length of life to the battery that came with the phone.
If you can you should take it back and get a new GS3 cause you should definitely be getting better battery life than what you are reporting especially with such low on screen time.