Shakespeare having multiple lesbian characters. Or rather, the assumption that many of his female characters mentioned in this article were intended to be gay.
Using the colloquial definition of a lesbian, and not the one put forth by Adrienne Rich, the only characters who might actually be lesbians are Viola and Olivia. And even there it's hard to determine how much of Olivia's affections was based on Viola or her made-up persona, one that was meant to be a man. And then, of course, the question becomes one what that says about lesbian desires. It would be easy to conclude that Olivia likes the male persona but wouldn't want the female body that comes along with it, which could be interpreted to mean that lesbians secretly desire masculinity, which is problematic.
Hermione from A Winter's Tale, Cleopatra from Antony and Cleopatra, and Beatrice from Much Ado About Nothing could be involved with their female servants or friends, but the evidence that they were is circumstantial at best. I would be more convinced if there was some evidence that Shakespeare was inspired by historical events that involved women loving women or stories of women loving women, since so much of what Shakespeare wrote was based on other sources.
The Renaissance play that actually has one of the most interesting depictions of a woman who hangs out with other women is The Roaring Girl. This play, too, has a problematic set of ideas about gender and women's place in the world.