Is the concept on the show unforgettable real?

Answer 1

Only in the abstract. There are people with "autobiographical" memory, but no one who can remember "everything" that they see and hear. People with autobiographical memory can remember certain details of each day of decades of their life, but the details are hardly exhaustive. Research into the phenomenon has shown that the feat is accomplished at the cost of their spending a large portion of each day remembering what they remember.

Even if such a person as the character on Unforgettable did exist, their memory would be subject to false memory syndrome and the other cognitive factors that influence our personal realities and the affect the clarity of our memories.

For more information try Higbee's "Your Memory: How it works and how to improve it".