The embryos
First, the genetic engineering itself may not work correctly. Choosing a certain type of gene, say for hair color, may turn off a different gene, say for aging longer (this would be telomerase, for the curious) (Agar). This type of problem may not manifest itself until the baby is actually born. Furthermore, the parents may not get what they expect. Hypothetically, they might choose a female embryo with fair skin, dark hair, and a minimal chance of disease, and get a healthy daughter who is fair skinned with dark hair who also has a terribly mean personality. Because "personality genes" are difficult to interpret and understand (they may not even exist!), the personalities of designer babies cannot be chosen for. The parents who wanted the fair and brunette daughter may have accidentally passed up a sweet tempered red haired son.
The choosing of embryos brings to the forefront a large moral issue with designer babies. Many embryos are created, and not as many are implanted into the mother. The embryos that do not fit the specifications set by the parents will get thrown away. Had these embryos have been allowed to grow, they could have had long and fulfilled lives, however the ones that are thrown away lose that potential life. Many people, especially those who are pro-life, view this aspect as a huge problem in the creation of designer babies. If many embryos are going to be thrown away, they should not be created.
Even embryos thrown away for