In British English, the word ‘pot’ is used as a verb to mean “to shoot small birds and animals without taking careful aim.” The reason you don’t need to aim is because there are so many birds/ animals clustered nearby, that if you shoot in their general direction, you are bound to hit something. There is no way that you can miss. Hunters took pot shots because they wanted to put food on the table; their aim was to fill the cooking pot! The opposite of ‘pot shot’, I understand, is ‘fair shot’; the kind of shot a ‘gentleman hunter’ prefers to take. In this case, the hunter decides which animal he wishes to kill, aims for it, and then shoots. As time went by, the term ‘pot shot’ began to be applied to any sort of blow – physical as well as verbal – that was difficult to avoid. The expression “take pot shots at someone” is now used to mean to criticise someone rather unexpectedly or unfairly.
*During the press conference, several reporters took pot shots at the aging actor.