Learn English – What’s a funny word for someone who is frequently breaking things

I would probably use amusing for this. From your description, I'm imagining a story or something else that is entertaining and has a humorous tone, but there's no one specific thing or moment that makes you laugh the way that the punchline of a joke does.

There are some more specific words that apply to certain cases. For example, this is how I usually think of the Mel Brooks film The Producers, about two men running a scam that involves producing the world's most terrible play - it's not funny because of jokes or one-liners, but just because their situation becomes increasingly absurd and ridiculous. In this case, the word farce fits well.

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.