Before you read, I'd like you readers to know that I'm quite the fan of both the original books and various interpretations including BBC's 'Sherlock' and that all opinions expressed in this are indended for amusing, not offensive purposes. If an opinion is stated here, it's not neccesarily mine (or yours, even if you use these), and the last thing I want to do is hurt anyone's feelings.
I hope that, with the above in mind, you enjoy!

1. You knew it was coming, so let's just get it out of the way... Tell them that Benedict Cumberbatch is ugly. Hideous, even. I personally think he looks fine, and maybe you do too, but ignore that. Do whatever you can to convey that you think his face is unnaturally bad. Write a poem or something, e.g.

Benedict is an actor from Britain
With whose looks many a girl is smitten
Though I cannot see how
For he looks like a cow
And his face I would much like to spit in

2. Tell them that, after extensive analysis, you have found that Martin Freeman is not in fact made of any of the following: kittens, jam, hedgehogs, jumpers, or anything remotely adorable.

3. "Forget" Mr. Cumberbatch's name, and come up with vaguely similar substitutes: Bandersnatch Cumberbund, Bendaroo Cucumberpatch, Bendelstick Batchabrownies, Engerbert Humperdinck, Stumblybum Stinkerpatch, the list goes on. Oodles of fun await you with this one.

4. Repeatedly make scoffing noises while watching the show with the Sherlockian. When prompted, explain that "The acting on this show is just awful!" Dodge the inevitable punch.

5. Get the actors' roles confused. Whenever Watson is in the shot, yell "TIM!" or "BILBO!" With Holmes, you can be extra annoying: "PETER GUILLAM! Why's his hair all weird now?" "THAT GUY FROM WAR HORSE! Where's the moustache?" Or, horror of horrors... "KHAAAAAAAAAAAAAAAAAAAAN!" Hey, I never said you had to be accurate.

6. Elaborating on #2, it's so much more effective when you compare him to an animal. Just not an otter, that will send them into fangirl mode. Some of my favorites include a sheep, horse, llama, giraffe...

7. Conversely, take advantage of his ever-changing hairdo to say things like "Oh, he's only cute with blond hair, he looks awful with this color."

8. Whenever Holmes makes a deduction, say "He Googled it." Whenever he explains how he made a deduction say, as dismissively as possible, "That's a bit of a leap."

9. Wait until whenever Holmes comes on screen and say "Hang on, where's Jonny Lee Miller/Robert Downey Jr.?" or that Elementary/the American movies are better.

10. Whenever you see a taxi (in the show, in real life, anywhere), point at it and yell "MURDERER!"

11. Play dumb. "So, wait... Holmes is gay? He's a detective? He's got a nicotine addiction? Watson's a doctor?"

12. Or... Play smart. Whenever the show contradicts the books, point it out and act outraged. "Why do they use first names?! No, Watson and Stamford got lunch, not coffee! Moriarty's old, and he's only in one story! Irene Adler's an American! Why isn't Mycroft morbidly obese?"

13. Another way to play smart: freak out whenever something in the original canon is referenced. And trust me, this happens a lot. You'll be talking through the entire show. "Oh, I remember the five pips, that's from The Adventure of the Dancing Men! Oh, this is like that part with Watson's watch from The Sign of the Four! Oh, look, he still keeps his mail stuck in the mantel with a knife!"

14. In continuation of the previous point, if both you and the Sherlock fan don't know very much about the original stories, make some up. ("Oh, yeah! The poisoned chocolate is from The Adventure of Willy Wonka's Mental Breakdown!"). If the fan is fairly familiar with the books, do some research. Wikipedia is your friend. Or if you're lazy like me, feel free to use the examples from #13.

15. Whenever any two characters are standing really close together, or look at each other for more than a second, or, in the case of Holmes and Watson, share a bromantic moment (or it's somehow insinuated that they're dating), say "Ooooooh!" in as obnoxious a tone as possible and nudge the Sherlockian. You'll find instances of all of these in abundance.

16. Refuse to like Holmes. Maintain that you think there's not a single redeeming quality in him. Not even the cheekbones.

17. Give characters nicknames. For Holmes: Shirley, Sir Boastalot, Fluffy, Freak, Arsehole, etc., for Watson: Johnnyboy, The Bachelor, Dummy, Shorty, Frumpy... The possibilities are endless!

18. Mention that every girl we see Watson date is out of his league.

19. Say you hate Molly. Your Sherlockian will be gobsmacked. For extra gobsmackification, tell them your favorite character is Sally Donovan.

20. Make ridiculous deductions of your own, as illogically as possible. Make them completely random and impossible to explain. "Well, Fred, I can see from your left shirtsleeve that your paternal grandmother has just had an unsuccessful knee replacement surgery, that it was unsuccessful because the doctor was an escaped Irish convict in disguise, and that the patient in the next bed over had herpes of the spleen." When they accuse you of making it up, say "But isn't that what Holmes does?"

21. This will be very mentally scarring, but it will scar your Sherlockian more than it will scar you: Ship It. The worst couple you can imagine. Give them a catchy pairing name and watch your Sherlockian scream in horror. Enjoy the moment, then bang your head against a wall until said pairing has been forgotten. If your Sherlockian genuinely, actually does like that couple, then I pray that Thor help you...

22. ... Or you could just tell them that John and Sherlock will never ever ever get together. Like, ever.

23. Make them read a Flowers in a Box-caliber Sherlock fanfiction in its entirety. Email it to them, text it to them, read it aloud to them if you have to. Again, self-destructive but priceless.

24. Regularly make references to the show. When the Sherlockian mentions it, act confused, as though you've no idea what they're talking about. Start with something somewhat vague, like imitating Holmes saying "Boooored" or "Obviously" and gradually work your way up to the obvious ones, like "What is this, a death-frisbee?" Continue to play innocent for as long as possible.

25. Confuse it with other BBC shows. This is especially applicable with the BBC because they always recycle their actors in as many shows as possible. So, for example, when watching the Hound episode, say "I think Henry's the hound because he's really a werewolf" or "Mycroft is secretly a genetic experiment gone horribly wrong, and Sherlock will have to get the Doctor (bonus if you call him Doctor Who) to help stop him."

26. In a similar vein, propose loony crossover ideas. "What if Doctor Who took Merlin and Arthur to help Holmes and Watson solve the identity of Jack the Ripper?" Better yet, go across the pond: "So, Holmes and Watson team up with Jethro Gibbs..." and maybe add some reality TV: "... And then they audition for America's Next Top Model..."

27. "So Sherlock isn't his last name?"

28. Confuse Mrs. Hudson with Irene Adler. "Why's their housekeeper naked?"

29. Whenever you say anything to them, say it in Moriarty's voice, Irish accent and all: "Hiiiiiiiiiiii, Aaaaaanna. Did you do the maaaaaath homeworrrrrk? Can I copy it? Pretty pleeeeeaaaaase? PLEEEEEEEEASE?!"

30. Write 'I O U' on a bunch of stickynotes and put them in places they can't miss: their stuff, their desk, etc.

Clearly some of these might be unwise to attempt... Use judgement, fellow annoyers! I myself frequently do #13 without intending to.
If you have any other methods of annoyance, by all means let me know in the comments section or PM me or something. Maybe we can gather enough for a sequel!
And please, if you were offended by anything at all that I've written, let me know and I'll almost certainly delete that part, and I'll definitely apologize. Thanks!