The MOEMS contents has 4th-6th grade divisions and a 7-8th grade division. The book you have may only have the elementary problems; I forget.
I've just started doing Math Olympiad problems (from the 2nd volume of the book) with my DS9 and other "highly capable" 3rd graders at his school. This is a 1 hour a week pullout, and we've only met once, so I don't have a lot of experience with it yet but the level of the problems strikes me as appropriately challenging for my group so far.
My experience with the problems is that many of them allow a slow brute-force (or calculator) solution, but also have an elegant and quick solution. They're intended to teach problem solving techniques (and the mathematics behind those techniques). Reading or discussing the solutions is pretty essential to getting the most out of them, I think. Once your son gets the hang of the book, I'd guess he'd love working on it on his own. But you might want to work a few sets of problems with him the first time, to make sure he's using the resource well.
If he doesn't think it is challenging enough, you might try doing the problems in the time limits suggested for the questions.
If these really are too easy, try the middle-school level. (Volume 2 of the book you have has the middle school problems, I know.) And if those are too easy, try artofproblemsolving.com I'm looking forward to getting this book when my DS is ready:
http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=100
