Ways to politely insult somebody's intelligence in Mandarin?
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.