The term half-wit is said to have been coined during the late 17th century to describe someone who believes he or she is truly witty and informed, but noticeably lacks the intellectual and social skills necessary. In the original sense, a half-wit would not necessarily be a dullard or an idiot, just someone whose reach on wittiness far exceeded his or her grasp. The meaning later shifted to include those who were indeed uneducated or foolish.
A half-wit is generally more high functioning mentally than a moron or an idiot, but the results are generally the same. A true half-wit might take on a complicated project but lack the common sense to correct problems along the way or foresee potential problems. The idea or project may be perfectly reasonable, but the execution could be considered half-witted. Building a new prison would be a laudable goal, for example, but locating it next to an elementary school would be the work of a half-wit.
The best way to describe a half-wit might be dangerously dumb. Unlike a true moron or idiot who cannot grasp the hazards of his or her actions, a half-wit may have at least a partial understanding of the risks and does it anyway. A half-wit understands what a stick of dynamite can do and how to light the fuse, but may not have the common sense to warn others before using it. A half-witted person is not necessarily mentally retarded, but often lacks the ability to think past the present moment.
The term half-wit is often used as a slur against people of seemingly normal intelligence who happen to have a brain fart at a critical juncture. When a plan which looks perfectly workable on paper fails in the real world because of human error or shortsightedness, many people wonder which half-wits should be held responsible for the failure. In a similar vein, a politically-motivated solution to a crisis may be described by critics as half-witted if it appears to be hastily conceived or poorly executed.