As all experiments thus far have shown, the biggest challenge with this surgery will be reconnecting the spinal cord. But that's just the largest hurdle in the operating room. A host of potential post-op problems need to be addressed, too.
If everything goes smoothly during the surgery (and that's a big "if"), the first concern after the operation will be head rejection. You don't want the body fighting against the head, so regular blood samples and biopsies will have to be performed to confirm no antidonor antibodies have been formed.
There's also the chance that the surgery will largely work and the head will get attached and accepted by the new body, but there will be smaller issues that didn't go so well during the surgery. For example, some nerves associated with the vocal cords loop down from the brain, down the neck and back up again. Reconnecting them may pose a larger challenge to the surgeons, and speech may be affected. The esophagus might not be totally leak-proof after reattachment, leading to potential complications with digestion.
Perhaps the biggest deal of all will be the psychological impact on the recipient of the new body. Unlike many other organ transplants, a full body transplant will always be visible to the recipient — a constant reminder that their body is not their own. Patients who have received hand transplants are an excellent comparison point, as they have an ever-present visible reminder of the transplant. These transplant recipients have had to figure out how to mourn the loss of their hand and come to terms with their sense of self and body image. And that's just for a hand. Imagine the degree to which an entire new body will affect the psychology of a patient. Even if someone is medically determined to be a suitable candidate for the surgery, a psychiatric evaluation will be a necessity to make certain they can handle their new life with a new body.