For cole henley, not tested, probably errors all over the place, but this was my general approach

gistfile1.js

function add_all_integers(i) {
	
	// i is an array that might contain arrrays, integers, strings, add all integers within it

	var total = 0;
	function add_iterate(item) {
		for(var counter=0;counter<item.length;counter++) {
			if(typeof item[counter] == 'object') {
				add_iterate(item[counter]);
			} else if(typeof item[counter] == 'number') {
				total += item[counter];
			}
		}
	}

	add_iterate(i);

	return total;

}

OK, surprisingly, running it in the console seems to suggest it is syntactically and functionally correct, wow, that's gotta be the first time ever for writing javascript - haha