He probably did not originate the term, as it must have started as a game, like a greased pig chase. Shakespeare did however use the phrase in Romeo and Juliet, which would have popularized it. Mercutio says:
Nay, if thy wits run the wild-goose chase, I have done, for thou hast more of the wild-goose in one of thy wits than, I am sure, I have in my whole five: was I with you there for the goose?
Romeo and Juliet act 2
Shakespeare did not use the phrase "a boiling idiot". You are probably thinking of "a blinking idiot", which comes from The Merchant of Venice.
Romeo and Juliet, Act 2 Scene 2
Merry Wives of Windsor. It's the same play that gave us "the world's my oyster".
The time period just affected Shakespeare's plays - come on.
WILLIAM SHAKESPEARE 'MACBETH AND THE THREE WITCHES'
In "Romeo and Juliet," Shakespeare uses the phrase to refer specifically to an erratic course taken by one person and followed by another. Later Samuel Johnson defined the phrase in his dictionary as "a pursuit of something as unlikely to be caught as a wild goose." So, over time the phrase has come to describe any fruitless pursuit.
Shakespeare's "The Tempest"
William shakespeare
Shakespeare did not use the phrase "a boiling idiot". You are probably thinking of "a blinking idiot", which comes from The Merchant of Venice.
Hamlet, Act 2 Scene 2
Romeo and Juliet, Act 2 Scene 2
The saying "Beware the ides of March came from William Shakespeare's famous play, "Julius Caesar."
'Coin a phrase' - 'Quoins' are used to wedge columns of type in the printers 'chase'. Printers believed to put things in type was to make them permanent and believe this to be the origin of the phrase, 'Quoin a phrase'. (this is not the only explanation though - there are several literary uses of the phrase too!)
None. The phrase 'He hath eaten me out of house and home" is from Henry IV Part 2 Act 2 Scene 1
The phrase "what the dickens" was coined by William Shakespeare and originated in The Merry Wives Of Windsor Act 3, scene 2, 18--23, it was an oath to the devil said by Mrs Page.
The phrase "blinking idiot" is not a direct quote from any of William Shakespeare's plays. It may be a modern adaptation or interpretation of a character's dialogue in one of his works, but it is not a famous line from Shakespeare's original text.
Shakespeare's pen.