<< What about his ability to see in the ultraviolet range? >>
This is the one part that I had a hard time thinking of a convincing enough explanation if you were to take the Mental Patient stance.
Possibile Explanation(?): Photosensitivity is not an unheard of phenomena. I'm very sensitive to light myself and prefer dark rooms to bright light and I even had to get heavily tinted perscription glasses so I wouldn't be blinded while outdoors. Robert obviously suffered from an extreme case of this, and perhaps his ability to see within the ultraviolet range was an abnormal phenomena brought on by either the trauma of his family being killed or a head trauma when he jumped into the river and tried to drown himself. Or maybe a combination of the two.
I know that's not very convincing, but the human brain is still a vast mystery and humans have been known to do abnormal things in abnormal situations or after having suffered some kind of brain injury. Things which seem pretty outlandish but which are later understood with scientific explanation. For example, a woman having superhuman strength to lift a car off her husband after he became trapped beneath it while changing a tire. Seems impossible but we now know that the rush of adrenaline made it possible for her to lift it just enough to let him crawl out; something she could have never done under normal conditions.
I wouldn't be surprised to find that more reasearch might offer an even better explaination. I'm not trying to convince anyone that he wasn't an alien. This seems to be the general consensus. For myself I too like to think he was an alien, but at the same time I like the notion that all this was a brilliantly orchestrated delusion extending from his psychosis brought on by the traumatic event of his family being murdered. I think I'm more fascinated by the excellent job of the writer and director to present a story in which either stance could be true.
Most stories end with a nicely packaged ending which leaves the viewer/reader without any doubt about its conclusion. This one, however, could be either way. If you choose to believe he was an alien, then you are requried to use what is known as "the suspension of disbelief" in order to believe in an alien being from the planet K-PAX since our current real-world knowledge provides no evidence that alien beings exist. If you choose to believe he was just a mental patient, then you do not have to suspend disbelief to accept something outside of our current knowledge, but you are forced to accept facts only as they are presented with speculation being your only recourse towards solving the mystery.
Ingenious writing indeed! The movie was based on a book. I think I'm going to track down the book and read it.