There is no rhyme in the sentence, but its rhythm is iambic, that is, one unstressed syllable followed by a stressed one. It is typical of English speech and frequently found in English verse. The sentence is also alliterative, in that three of the five words begin with the sound /k/. Alliteration was a feature of Old English verse, and it still appeals to the ears of English speakers. It may be these features combined that you, and perhaps others, find pleasing. It has to be said, though, that the sentence, which has its origins in Britain in the Second World War, has been done to death.
I don't know of a phrase where someone can so generically point out a flaw. In your example, I'd say human - nobody is perfect. Perhaps his weakness or limitation would fit here.
There are words for dramatic flaws.
An Achilles heel: a portion, spot, area, or the like, that is especially or solely vulnerable. It does not need to lead to his downfall; it connotes someone who is pretty damned perfect except for this one thing. "Tom Cruise has an Achilles heel" would be understood that way.
His Achilles heel is his quick temper.
Shortcoming, or foible would be understood as an understatement; if he's crazy, that's a major problem; to call it a foible before stating the flaw would be mildly sarcastic.
A tragic flaw in drama is a failing of character in the hero (someone of high repute/honor/etc.) of a tragedy that brings about his downfall. Regarding Hamlet:
He has exceptional qualities like graceful personality and popularity among his country that is eminent. His tragic flaw is his delay in action and irresolution...
Other expressions for this are simply flawed, or inadequacy.
Best Answer
The phrase warts and all springs to mind. This was supposedly used by Cromwell to his portrait-painter to discourage a flattering representation.
It has come to be applied to something that should be accepted in its entirety, good points as well as bad.