Hi,
I'm having the same issue here. Almost identical, but in mine, the right side does work with certain plugs when you move them around a little, but if you move them again the right side stops working. Have tried with many headphones, car auxiliar cable, factory headphones, and two of them were intermittent on the right side. The others just worked on the left side.
I slimmed a Q-tip down a little and removed a lot of dirt out of it, and nothing. Then, I used a toothpick to scratch the bottom of the jack and this giant piece of fluff and dirt came out. Went to try it again and still no luck. I looks like the jack is somehow loose or not making proper contact for some other reason.
I read that someone fixed a similar problem by removing the back cover and tightening the screws near the headphone jack. I haven't tested that yet because my screwdrivers won't fit.
Any suggestions?
Samsung Galaxy S3 i9300 (rooted).