I got my phone recently, 2 weeks ago I guess. I have a similar issue, and wondering if you also experience this on your phone (I guess in addition to your static). Using any other headphone I tried (non-stock), when I plug in the jack (all the way of course), the contacts don't appear to connect properly. So, if you move the plug to the left, it appear to connect, if you let go, it appear not to connect well. This is also affecting the auto-headphone connection by the system.
Now, if I take the Samsung headphone and plug it in, it works perfectly, sort of. If I move it to the left, it still works, if I move it to the right, it stops working. If I move the cable around, it does cause static. If I shake the phone around, there is no static, so the connection appears solid (without physical movement of plug).
This may be related to your issue, where the contact is not good. Can you try the same and see this is happening. Can anyone using with headphone confirm this is a hardware issue with the headphone jack, or is this a common issue with the S3 headphone jack, where certain plug types work, and some don't. The ones I've tried where it doesn't work has the 2 lines only, the Samsung one has 3 lines.