The Irony of Being Legitimate
Once it is discovered that Irving does have legitimate documents to prove Howard Hughes did employ him to write his autobiography, everyone believes it as truth. The irony is that it isn't. While the documents gave him credibility, he admitted that he fabricated being hired by Hughes. Thus, his fakes, because they were given legitimacy by "experts" made him credible, and the public bought it.
The Irony of an Accusation
We are introduced to Irving early on in the film as he is accusing Elmyr of being a fraud. That he has for years created fake masterpieces and sold them on the art market. The irony is that Irving himself is a fraud. He forged an autobiography about Howard Hughes which he later admitted to.
The Irony of the Expert
What we learn from this film is that Elmyr has sold many of his paintings, which are fakes of masterpieces, to museums all over the world. The irony is that these museums and the people that curate them are meant to be experts on art. Yet, they have purchased fakes and hung them in their galleries for years, telling the public that they are the real thing.
The Irony of a Trusted Narrator
Welles opens this film by saying that he is going to tell us the facts. With his charisma, and his editing we begin to trust Welles to tell us the truth. The irony is that Welles only promised to tell the truth for the first hour of the film. The last 28 minutes he creates a completely fabricated story to add to trickery of this tale, and we are left to understand that art is about using lies to reveal a truth.
The Irony of Howard Hughes
Throughout the film we are shown footage of Howard Hughes as he plays an active role in this tale. Welles shows us footage of him in the middle of the film in order to create the reality of what was happening in Hughes' life. The irony is that Welles used stock footage of the actor Don Ameche playing Howard Hughes. Thus, another fake is placed before us in a movie about fakery.