That is an excellent website with a great article.. I don't think left and right twist is something we generally have to worry too much about, but when you happen to have a spool of "S" twist rather than "Z" twist it can curl up on itself and cause you to have broken threads. Always a bummer when you're stitching away happy as can be. I have turned the spool over, putting the end that was on the bottom on top and that eliminated the problem at times.. I also think the rule of thumb is that stacked spoola should be put on the spool holder and the tread unwound off the side.. while with cross wound spools the thread should come off the end..
When you're hand sewing or quilting and the thread keeps knotting or twisting and seems hard to work with.. Try cutting the thread and re-threading the needle with the other end of the thread.. Thread likes to go one way and will balk at being used in the wrong direction.
Interesting topic, hopefully some problems will go away with the information here.