Where has he been dishonest?
I think he can be a bit myopic with regards to many of his pronouncements, but dishonest hasn't been my impression of him.
He's said the Canadian bill of human rights, C16 was a bill that allowed prosecution for somebody to criticise a persons choice of fashion as hate crime. It's not. The C16 bill just adds gender to the list of things that are admissible to prosecute for when it comes to hate crime. So if you murder a transvestite holding a Nazi flag you will be convicted for murder, as we as a hate crime. Or if you you say "death to all transvestites, lets go a murder them". That can also be construed as a hate crime. Saying that you think that gays and trannies are bad people and wrong is not a hate crime under C16. Jordan Peterson just lied. Also, it's already been added to the territories specific hate crimes list. So all they did was to clean up the law code and make a popular law around the country as a federal law. So it won't even change anything.
He also claims that now he's forced to use the pronoun that somebody wants to have, otherwise he can be charged with a hate crime. Not true. There's no sanction. He's also said that he thinks that these new pronouns is a conspiracy by the marxist left to... do something? He's a bit hazy on what. I think that teenagers wanting to be called this, that and the other is perfectly fine. Teenagers struggle with identity. It's what being a teenager is about. Calling that a marxist conspiracy is absurd.
He's also said that he's been threatened by his university by being fired if he didn't obliged. Not true. They asked him nicely. And just to make it super clear, they wrote three whole paragraphs about they being committed to freedom of speech and academic freedom. Just so there shouldn't be any confusion.
His talk about social justice tribunals is ludicrous.
That said, I think he's just an enthusiastic intellectual, who makes a wee bit too much of an effort to make an impact. He would do good to reign himself in a bit and stick to things that are actually true. He conflates what he worries might happen in the future, with what has already happened.
That said I think he's said loads of clever stuff. I agree with him to a large extent.