At the end of Harry Potter and the Goblet of Fire, we learn that who we thought was Alastor "Mad Eye" Moody, was actually Bartemius ("Barty") Crouch Jr, who impersonated him through the use of Polyjuice Potion, for the entire book. We've never met Mad Eye Moody.
He fooled us all — the readers — just like he fooled Dumbledore, an old friend of Moody's, so he must have imitated the real Mad-Eye quite well. He may have been acting out of character when he punished Draco by turning him into The Amazing Bouncing Ferret (although that's not certain); it probably wasn't out of character for him to teach the Unforgivable Curses to fourth years.
What was completely out of character, and what tipped-off Dumbledore in the end, was how he separated Harry from the rest just after having returned from the graveyard, with the dead body of Cedric Diggory in tow.
From what I remember, in the subsequent books, the real Mad-Eye Moody doesn't seem much different from the fake one. Even though we've just met him, it feels as if we've known him longer, but that wasn't Moody, that was Barty. Harry's (and our) history with him doesn't go back to the Triwizard Tournament — that was Barty.
So how does "Mad Eye Barty" compare to Mad-Eye Moody? What mistakes (if any) did he make?