Could unwanted magnetism be part of my soldering problem?
Adding to all previous comments, my experience is to avoid cheap (hobbyist) irons altogether as they do not reach a high enough temperature and cannot maintain that temperature when the tip is presented to the job very well. A tip that is clean and tinned (but not running with solder) should be presented to heat the joint slightly prior to the solder being applied and if the iron is hot enough and the component and board are clean, the solder will flow and it should be possible to do it in around a second. There should be no balling at all. My advice is to invest in a Weller or similar make iron if you are doing a lot of soldering and avoid the cheap ones altogether.