Of course there are.
Henry V
Hotspur- My horse is my mistress.
Or pretty much anything from Venus and Adonis, really. 
Agree with Chronos, incidentally, on Mistress Quickly. How about this exchange from 1 Henry IV?
MISTRESS QUICKLY: …I am an honest man’s wife, and, setting thy knighthood aside, thou art a knave to call me so.
FALSTAFF: Setting thy womanhood aside, thou art a beast to say otherwise.
MISTRESS QUICKLY: Say, what beast, thou knave, thou?
FALSTAFF: What beast? Why, an otter!
PRINCE HAL: An otter, Sir John! Why an otter?
FALSTAFF: Why, she’s neither fish nor flesh; a man knows not where to have her.
MISTRESS QUICKLY: Thou art an unjust man in saying so: thou or any other man knows where to have me, thou knave, thou!
Possibly this exchange about “her c’s, u’s and 't’s”?
Oh, and this little bit from Henry V; I’ve heard it done to good effect.
If I could win a lady at leap-frog, or by vaulting into my saddle with my armour on my back, under the correction of bragging be it spoken, I should quickly leap into a wife. Or if I might buffet for my love, or bound my horse for her favours, I could lay on like a butcher and sit like a jack-an-apes, never off.
What, nobody’s mentioned the scene in Titus Andronicus where the empress gives birth to a black child and her two older sons confront Aaron the Moor?
“Thou hast undone our mother!”
“Villain, I have done thy mother.”
And, from Timon of Athens:
Painter: “Y’are a dog.”
Apemantus: “Thy mother’s of my generation. What’s she, if I be a dog?”
You are a son of a bitch.
My favourite sonnet is #151, which is essentially an ode to his penis:
flesh stays no further reason,
But rising at thy name doth point out thee
As his triumphant prize.
Zombie Shakespeare!!
Is this the end of zombie Shakespeare?
Best euphemism for sex since “making the beast with two backs.”
There’s a scene in Henry V where the French princess is brushing up her English - aware that a diplomatic marriage is likely - and discovers to her scandalized delight that English has the words “foot” and “gown” in it, which (especially as she pronounces them) sound like the French for “fuck” and “cunt”. But she diligently repeats the whole lesson including the dreadfully naughty words. 
Polonius: Do you know me, my lord?
Hamlet: Excellent well; you’re a fishmonger.
Polonius: Not I, my lord.
Hamlet Then I would you were so honest a man.
Polonius: Honest, my lord!
Hamlet: Ay, sir; to be honest, as this world goes, is to be one man picked out of ten thousand.
Polonius: That’s very true, my lord.
Hamlet: [Reads] For if the sun breed maggots in a dead dog, being a god kissing carrion, — Have you a daughter?
Polonius: I have, my lord.
Hamlet: Let her not walk i’ the sun: conception is a blessing: but not as your daughter may conceive; — friend, look to 't.
Polonius: [Aside] How say you by that? Still harping on my daughter: — yet he knew me not at first; he said I was a fishmonger: he is far gone, far gone: and truly in my youth I suffered much extremity for love; very near this.
This one cracks me up everytime. Fishmonger=pimp.
SFC Schwartz
One of the dirtiest jokes in Shakespeare, in my opinion, is a line that rarely gets a laugh in Twelfth Night: Malvolio’s description of his lady’s handwriting. He references her “C’s, her U’s, and her T’s, and thus she makes her great P’s,” clearly referencing the word “cunt.” Aguecheek emphasizes it, asking “Her C’s, her U’s and her T’s: why that?” Audiences don’t seem to get it, as though they don’t think they should be laughing at a “cunt” joke at a fancy Shakespeare play.
I’ve never heard that, but there is a point where an infatuated Claudio asks Benedict if all the wealth in the world could buy such a jewel (i.e., Hero), and Benedict replies, “Yea, and a bag to put in into”. There’s some speculation that’s a play on pudenda. I’m not sure I believe that, but it has the advantage of vague plausibility over your researcher’s theory. 
It’s at least clear that Benedict is discounting Claudio’s love, and making a not-so-veiled reference to prostitution.
This is the problem I have with most of Shakespeare’s jokes. They just aren’t that funny. I’m sure they were hilarious at the time, but now they just seem childish. “He spelled out CUNT! OMG!”
I hear what you’re saying – the delivery is completely different from what we’re used to these days. The topic is really no different from the “See You Next Thursday” jokes that get made now.
Nunnery was slang for brothel.
Sweet mother of mercy!
Which is ALSO from Shakespeare.
Capulet: bring me my sword, ho!!
Haha love that line:)