One sandwich short of a picnic
A jokey, colloquial term for stupid.
There are many phrases of the form 'an X short of a Y'. These all mean the same thing, that is, the person being spoken of is stupid. The 'short of' insult began in Australia and New Zealand in the mid 19th century; for example, Colonel Godfrey Mundy's Our Antipodes, 1852:
"The climate is productive of chronic diseases rather than acute ones. Let no man having, in colonial phrase, 'a shingle short' try this country. He will pass his days in Tarban Creek Asylum."
Of course, shingles are wooden tiles and many of these phrases refer to having something loose or missing 'up top' - 'a few slates missing', 'a screw loose' etc.
'A sandwich short of a picnic' is fairly recent. The first citation of it that has been documented is from the BBC's Lenny Henry Christmas Special, December 1987. In that, Henry performed I'm Mad, a spoof song and dance routine written by Kim Fuller and others. This aped Michael Jackson's 1983 hit Bad. Henry, in a straightjacket, sings 'I'm mad, I'm mad', while the backing vocalists sing:
He's mad, mad, one brick short of a load
He's mad, mad, one sandwich short of a picnic
I have been informed by a correspondent that the 'two sandwiches short of a picnic' version of the phrase also occurs in the March 1987 film Walk Like A Man. with Mandell from early 1987. Christopher Lloyd's character is said to have uttered it, referring to the character played by Howie Mandell. Unfortunately, the film was such a turkey that it is now unavailable for sale and consequently I've not been able to confirm that report.
Other 'One' phrases: