There is no chance that Edward de Vere, the Earl of Oxford, wrote the plays attributed to William Shakespeare.
That said, I found the movie Anonymous to be reasonably watchable, although I thought many of Vanessa Redgrave’s scenes as the older Queen Elizabeth were ridiculous. But since the movie claims (perhaps as a joke) to be seriously advocating the position that Oxford wrote the plays, I was surprised that they did such a poor job of supporting the theory.
Oxford was shown as being tutored at length on topics other than poetry. He traveled abroad, he intrigued at court. When would he have had time to write the plays and the sonnets? The movie essentially presents Oxford as being mysterious gifted by the ability to write; he speaks of continual voices in his head. That could happen to anybody, and perhaps describes the real Shakespeare–if anybody could have written Shakespeare’s plays, then why not Shakespeare himself?
Oxford is shown as using the plays to support his court intrigues. Is it possible to imagine Shakespeare, with his clear vision of humanity, thinking that he could achieve such ends through his plays? One of the strongest examples of that in the movie was the suggestion that it was odd that Shakespeare portrayed Richard III as a hunchback, but even I know that Richard III was popularly (and probably falsely) considered to be a hunchback long before Shakespeare’s time.
Of course it’s conceivable if unlikely that somebody else wrote Shakepeare’s plays. But the undercurrent of the Oxford theory has always been that a member of the nobility would be more likely as the playwright than a commoner. But this reverses reality. The nobility were highly trained from birth in their roles in society. They were busy people with lots to do. It was far less likely that an earl could write the plays than a member of the middle class. As far as I know only one member of the English nobility ever achieved any note as an author: Lord Dunsany, who lived much later.
The movie did have a couple of nice (non-Shakespearean) lines, one of which, by the Ben Jonson character, was simply the truth: the only reason future ages remember the people who lived then was because they were alive when Shakespeare was writing.