Jack Lynch, in BECOMING SHAKESPEARE (2007), quotes some of the first to mention Shakespeare.p77
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[...A] contemporary playwright took aim at his rival in 1592, complaining about "an upstart crow, beautified with our feathers[...,]with his tiger's heart wrapped in a players' hide, supposes he is able to blast out a blank verse as the best of you."
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[I've updated orthography in the above, btw.]
Maybe this was tongue in cheek, though? (Although Shakespeare expert Lynch doesn't imply this, so probably not.)
Still I think it is interesting to look at the Bard of Avon's rep among his contemporaries. One of a number of poets at the time who dramatized pre-existing plots for the stage, "Shake-scene" (as the dude above playfully called him) apparently wrote with an ease of composition that marveled his theatrical company. Ben Johnson [according to Wikipedia] said, "I remember the players have often mentioned it as an honor to Shakespeare, that in his writing, whatsoever he penned, he never blotted out a line. My answer hath been, 'Would he had blotted a thousand,'[...]."
...So, Shakespeare was a very impressive wordsmith who, still, was thought a bit rough?
One more quote from Lynch
pp79-80
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!n the 1660s Shakespeare had some passionate defenders, but most common readers would have placed him last on the list. Not that they disliked him, but few would have put him in the very first rank. [If] Beaumont and Fletcher (who often worked together as a team) [...]were the people's favorites, Ben Johnson was the critics' choice.[...] Shakespeare[...]was sloppy. He lacked a university education. His flights of fancy sometimes passed the bounds of plausibility. He improperly mixed serious and frivolous scenes.
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So, according to Lynch, 17th C. English literary folks thought Mr. Shakes basically in the running, for their esteem, if not at the very, very apex--and in popular acclaim he registered in about the same area. (Yet, reading between the lines, Shakes was probably more popular than Ben Johnson and more esteemed by the literary folks than were Beaumont and Fletcher?)
In any case, Lynch goes on to explain that Shakespeare HAD been universally praised, even in his OWN time, for being very clever and funny, for creating very evocative expressions of thought and for producing phenomenal characterizations. (And these were things that, of course, contributed greatly to the Bard's great popularity in coming centuries.)