So I recently heard about this syndrome which states that there is some sort of a problem with chromosome 17. But also that it is typically not inherited but occurs in problems with reproductive cells (sperm or egg) or in early fetal development. How would such a mutation occur?

If the 17p micro deletion is not inherited, then it is a sporadic mutation. It sounds like the micro deletion may be acquired during fertilisation in the sperm or the ovum, or at the zygote stage? All ESCs in the blastocyst are still pluripotent so sporadic mutations here may still affect all three embryonic layers.