Ways to politely insult somebody's intelligence in Mandarin? I know of many words to insult people and call them stupid, but a majority of them are incredibly offensive. There are more polite phrases, such as 真笨, which I've seen used within families (as a plain 真笨啊！）, but nothing which seems the right level of formality for the context in question.

In English, the nearest equivalent of what I'm looking for would be along the lines of "fool", but not quite as strong as "imbecile". Something you can use in a formal situation, but something that won't incredibly offend the listener; more a "silly you" with a higher register of formality.

I'm not sure which words match this closely, if any exist. What words are closest to this meaning?
I don't know if there is a way to politely insult someone's intellect, that almost seems like an oxymoron to me. 

糊涂 (silly) is the only expression I can think of that doesn't stigmatize the addressee too much. But I would under no circumstance apply it to my boss or my in-laws or a teacher or anyone with whom one has to be respectful. 

E.g. 你这么糊涂! How silly of you!
Also: 糊涂虫

傻 is still somewhere between 'silly' and 'fool'. A mother could reply to the naive questions of her child with 傻孩子！ (Silly kid!). 
别犯傻！ (Don't be silly) is another way to use it. 

傻瓜 would a bit stronger, but between peers could be still acceptable, but I would only use it if it is clear that I am not really meaning it. 

胡说！ can used if you think someones says something stupid. 

By contrast 混蛋 and 笨蛋 are more verbal and far more insulting. You can see and hear movie protagonists spitting and yelling this at each other. 

UPDATE: 二货 is another non-offensive way to call someone silly, e.g. 二货朋友 a silly friend.