I once wrote an article on this topic for Writer's Journal. For a main character to be believable, he must not be too perfect, too flawless, and he should not know more than a real human being can know. If one person has a perfect understanding of quantum physics, microbiology, trigonometry, auto mechanics, and every Harlequin romance ever written, I can't accept him/her as a believable character.
Also each character must have both good and bad points to his character. Even Adolf Hitler--despite his devilish nature--had qualities that endeared some people to him.
Characters must also have weaknesses. Superman couldn't endure green kryptonite, and Frodo Baggins slowly succombed to the lure of the One Ring. If a character has no weakness, then the reader is assured he cannot be harmed or foiled, and the story stinks.