EXTREMELY easy. I'm surprised it hasn't started happening frequently already. As much as we (as a society) demonize people for even being suspected of this crime, I'd hesitantly say it does happen frequently already.
It would not be easily discovered as everyone in the chain of justice is quick to assume the defendants are guilty, and may not do as thorough a job as they should looking for evidence of a setup. Easier to parade around your captured "predator" and get good press, then to search for the truth.
I've seen it firsthand; an old buddy of mine admitted one day that when he was 19, he got drunk at a party and slept with a girl who lied about her age by a single year. She was 17, not 18, which is under the legal age in my state. Today, he is a registered sex offender, cannot vote, has trouble finding work, and cannot live in most communities. He has to inform the communities he is allowed to live in, which makes everyone immediately assume he's some kind of monster after their children.
Was my friend kind of an idiot at 19? Absolutely. But does he deserve to become a lower class of society for the rest of his life over his (ultimately harmless) mistake?