I think it is not just diplomacy, but more about the relationship and the history of sharing humor together that determines whether you can successfully use this idiom with someone or not.  With my friends who I know generally respect me and do not generally  treat me as if I am stupid, if I do something mindless, neglecting to pay attention to something, they could say:  ¨the lights are on but nobody is home¨ or ¨one sandwich short of a picnic¨ and we both would laugh.   Other than those situations, where those idioms are most often heard is on sitcoms on TV.  In real life, you should be very careful about when to use those idioms.

I remember a similar discussion about not the sharpest something, and my local version of it that is ¨not the sharpest tool in the shed.¨ Sometimes my husband will say that to me to lighten the situation.  If he does it appropriately with the right tone, it just helps me ¨child out¨ when he teases me.  

Here's the Australian version:

'He's got a few kangaroos loose in the top paddock'.

It is the same as 'he's got a few screws loose'.

One fry short of a Happy meal is good; I've never heard of it.

Others in the same trend: 'He's not the sharpest pencil in the case''

I think English is colourful how it diplomatically describes a situation/person in oblique terms, to convey an idea without causing offence, as you would if it were plain criticism or a plain/blunt description.

Haha yes, I have heard the one fry short of a happy meal. I'd forgotten about it! often changing this idiom up can be quite funny. 

Good try Bing, I can see where you are coming from! 

These idioms mean you don't think a person has a very good mental capacity or not all there.  They describe someone who is a little bit slow to get an idea, or not very good at figuring out fairly obvious things. . Sometimes, it could be used if you think someone is a bit strange!