Finding the next XML element
How about don't go to the next element before the loop, just check for the counter to reach zero, get the next element first in the loop, and the use a conditional operator to determine how to change the counter:

skipElement : function() {
  if (this.eventType !== Jsonix.XML.Input.START_ELEMENT) {
    throw new Error("Parser must be on START_ELEMENT to skip element.");
  }
  var numberOfOpenTags = 1;
  var et;
  while (numberOfOpenTags &gt; 0) {
    et = this.nextTag();
    numberOfOpenTags += et === Jsonix.XML.Input.START_ELEMENT ? 1 : -1;
  }
  return et;
}