I have the same problem with my S3. I found longer USB leads seem to be worse. So I took a very short lead cut the +ve supply wire and measured the charging current. It seems that the current fluctuates.
Test 1
When the S3 LCD is off (sleeping), I plugged in the USB charge lead. The measured charge current was very low (a few hundred milliamps). This seemed repeatable.
Test 2
With the phone swiped and the screen showing the icons. I again plugged in the USB charge lead. The charge current was much better. This time above 600mA and constant. This charge current remained when the LCD went dark and charged in 2 to 3 hours.
Test 3
With a very long lead (1 Metre and thin cable) The charge current measured was again 200mA. This was the case with the LCD on or off before plugging in the USB. I conclude the charging circuit has either failed in my phone or it see's a lower voltage and draws less current. In this mode the phone didn't fully charge even after 20 Hours!
Seems to me to be a software and possibly hardware design issue rather than a bad USB socket. Just my view.
Mark