Similar to Aspartame, one of the breakdown metabolites is phenylalanine, implying that those with sensitivity to phenylalanine or PKU may need to avoid it, however, the amount of phenylalanine produced when ingested was felt to be fairly negligible.
My interest was peaked by the fact that Advantame does not raise blood sugar or insulin levels in the multiple animal and three humans studies reviewed here and here. This implies that it probably won't cause weight gain and the studies in animals actually revealed some negligible weight loss.
The FDA claims this is a very safe artificial sweetener due to it's intense sweetness and requirement for only small quantities to be effective. In fact, Josh Bloom from the American Council on Science and Health was quoted saying that, "About the only way this stuff could harm you is if you were run over by a truck that was delivering it."
From the perspective of weight loss, this may be another sweetener that could be used effectively on a carbohydrate restricted diet.