This is an oft-repeated comment about Shakespeare that is partially based on some misunderstandings of language history. If you look through the Oxford English Dictionary, you’ll find about 1700 words for which the works of Shakespeare are the earliest citation. Does that mean that Shakespeare coined them? Not really. There are several problems with this.

It’s known that for the period in which Shakespeare’s works were published, the OED has a predilection for preferring Shakespeare as the author cited to show a word in that particular usage. The same is true of Chaucer, earlier in the language. That will lead to a preponderance of Shakespeare listed as the first cited reference.

“First cited reference” simply means that. It doesn’t mean the word was coined then. A good example of this, closer to our time, is that movie Bringing Up Baby (1938) is the first citation for the word “gay” in the modern sense. But, when Cary Grant used it, there was this expectation that the audience would get it. It’s clear that gay men were already using the term, just not in any print or recorded source that has been found. I had a professor who once said, “maybe tomorrow, someone opens a trunk and finds an earlier manuscript that contains “Beowulf.” Maybe tomorrow, someone publishes a journal from the early 1930s in which someone used the “gay” in the modern sense.

Again, gay men didn’t invent the word “gay.” It’s a fourteenth century loanword from the French, but they did create its modern meaning. Some of those 1,700 words are nouns used as verbs, and “to [noun]” is easily understood as “to act in a manner typical of a [noun].”

It is certainly possible that Shakespeare came up with some neologisms that subsequently became part of standard English, but it’s not something that can be determined. There are cases where we know someone coined a term. Most of these don’t become part of the language. That internet favorite, lists of “words that should be revived” are typically eighteenth century “inkhorn words” which were deliberate creations which writers tried to promote, typically in vain. That seems to be the opposite of what Shakespeare was doing.

That said, a playgoer in Elizabethan England might not be assured of understanding every word said on the stage. Shakespeare’s Henry V has an entire scene in French in which Princess Catherine’s attempt to learn English leads to words that sound dirty in either English or French. That said, it’s an easy assumption that his audiences weren’t saying “why does this Shakespeare guy keep making up words?”