That solder doesn't appear to have any flux in it. You can get rosin-cored solder from radio shack for pretty cheap.
The rosin in the solder will remove the oxide layer on the contacts so there is a better joint as solder does not bond well to oxides well.
First of all though, you may want to get some solder wick (which is really just copper wire) to remove the remaining solder from the holes. You do it by placing the wick onto the solder you want to remove, then place your iron on top of it. It may be a bit difficult to get the new jack in if you don't do this first
The rosin in the solder will remove the oxide layer on the contacts so there is a better joint as solder does not bond well to oxides well.
First of all though, you may want to get some solder wick (which is really just copper wire) to remove the remaining solder from the holes. You do it by placing the wick onto the solder you want to remove, then place your iron on top of it. It may be a bit difficult to get the new jack in if you don't do this first






