Barty Crouch Jr is stated to be an extremely skilled and intelligent. He's mentioned as having performed excellently on his exit exams in his 7th year. Voldemort also would have thought enough of him to brand him with the dark mark.
The real Moody was under the Imperious Curse the entire year. Crouch probably kept poking him constantly for information on how to act and what to say.
The real Moody gained a reputation in his old age of being unbalanced.
Dumbledore is human, and probably just plain didn't suspect it, particularly with everything else going on that year.
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Not removing this until Mega Man 64 is released on the Wii Virtual Console. Started on: 12/1/2009 https://imgur.com/mPvcy