Okay, let me explain this to you, nice and simple little boy:
No way to defend against her past level 3 + a dash every 2-8~ seconds(based on when she AA's, so quite possibly every 2 seconds, that also upgrades her next AA) + a stealth that can also stop AA's mid-animation as well as confuse the human mind by making them think she went one way then having them put their cursor there only to find she's completely the opposite direction = Broken OP.
Don't even need to say anything else.
She can literally dual almost any champion in the game. I've seen her win 1v1's with a late-game Yi and I'm sure many people can say the same.
"But her range is low"
http://leagueoflegends.wikia.com/wiki/Range
She's tied with 25 other champ's range, and is above 31 other champs and is only below 10 champs- one of which is tied with her at level one, and the other is below her until using an ability(Jinx's Switcheroo turning it into the rocket, otherwise her range is less).
"But she has a bad early game"
Yeah, up until she gets her BotRK, and sometimes even then against really bad early game champs.
And before she gets her BotRK, and heck, even after, she has a super safe laning phase with a dash most commonly attained at level 1, and a knockback and could-be stun at level 3, maybe 2 if she gets it(but usually Vayne players don't until level 3).
"But her main source of damage is every 3 attacks"
...
I haven't heard this many times, but when I do, I just cry.
Like. No.
NO.
NOOOOO.