Here in Germany I can call someone an idiot with included "grading": I can load it with surplus despise ("Sie Vollpfosten!"), or I can make it almost tender using dialect ("Du Döspaddel!"). I once made the error of calling someone a "baka" on the Internet, I thought the whole context made it obvious the second variant was meant. Fail.
I would be very surprised if Japanese doesn't have the same possibilities as German here. So, how could you vary the baka making the sense obvious even outside of face-to-face communication? (I guess if a friend says it to another with a big grin on a face, it can't be misunderstood - or are Japanese customs of interaction totally different?)
Note there are even more German connotations of the "mentally challenged": the "Tor"/naive (think Perceval) and the "Narr"/jester (think Nasreddin). Google Translate, which I never trust in such a case, gives "naibu" for the former (no translation at all) and "baka" (sic!) for the latter. (And I if I enter it in English, "dokeshi". Which rather seems to be a clown. But that's the "institutionalized" version - Nasreddin rather would be a "Schelm" - "fusei"?)
You see, a lot of fine distinctions I can handle without problem in my mother tongue, but already not even in English. How would you make these distinctions in Japanese?