Desoldering a tricky DC jack
The jack is faulty, so... 

Cut all the plastic away with side cutters, leaving just the metal terminals. Now you can remove each terminal separately. 

Hold the circuit board vertically in a vise. Get your iron hot as usual, and apply more solder to the pad to improve heat transfer. Grab a terminal (on its edge to reduce heat transfer) with your pliers, then heat the pad with your iron. The solder should melt quickly, then you simply pull the terminal out of the board. 

Finally, use a solder sucker and/or desoldering braid to remove excess solder from the hole.