I think Keith Olbermann may have had something to do with popularizing this Shakespearean expression.
In July 2005 Olbermann, writing about the London bus bombing, wrote:
July 21st may turn out to be the day the terrorists began to blow themselves up — hoist themselves, as the Middle English phrase goes, “on their own petard.”
I can’t guess why he called it a “Middle English phrase.” The expression, meaning “blown up by his own bomb,” comes from Shakespeare’s time (1605). By then, Middle English had morphed into Modern English.
As recently as Election Eve 2008, Olbermann was still using the phrase:
I’m trying to give Gov. Palin out there, a couple more seconds to figure out how she managed to get herself, as Shakespeare wrote of people destroyed by their own evil plans, “hoist with her own petard.” Keith Olbermann October 31, 2008
Here is how the expression is used in Hamlet (III, iv, 206-208):
For ’tis the sport to have the enginer
Hoist with his own petar, an’t shall go hard
But I will delve one yard below their mines,
And blow them at the moon.
Hamlet is talking about his old college chums Rosencrantz and Guildenstern. They’ve been spying on him for the king, and Hamlet suspects they are laying a trap for him. He’s planning his own preëmptive strike.
A “petar” was an explosive device. It got its name from the French verb pêter, which means “to break wind.” The Old French noun pet means “fart.” Shakespeare was making one of his earthy puns here.
Note that in the original expression, hoist is a verb in the past tense. Writers who want to use the expression correctly need to keep that fact in mind.
The “hoist” of current English usage retains the same meaning, “to raise, to lift up,” but in modern usage, the past tense form has been regularized to “hoisted.”
Ex. The crane hoisted the girder into place.
Commentators who don’t know their Shakespeare get it wrong:
The amusing context for this interview, was watching Keith Olbermann hoisted on his own petard. –Donklephant, March 15, 2008.
I mean who are the REAL victims here? CBS News has been hoisted on its own petard… –“Cecelia,” commenting on Dan Rather scandal, January 24, 2005.