Cooper Being Murph's Ghost (Situational Irony)
We see Cooper and Murph in her room early in the film as she believes there is a ghost sending her messages through her bookshelf with Morse and binary code. Cooper soon after decides to leave Earth as a pilot for NASA on a mission to find a habitable world, but Murph doesn't want him to go. He tells her he can't be her ghost. The irony is that we find out later in the film that he is in fact her ghost, as he is the one sending messages to her from behind the bookshelf.
The Lauding of Dr. Mann (Situational Irony)
Dr. Mann is considered 'the best of us' by those at NASA as he flew one of the original Lazarus missions to find new planets. The irony is that even the best of us, when left in absolute isolation, can become the worst of us. We see this as he kills one of his own and nearly destroys the ships and space station in an attempt to ensure his personal survive.
The Irony of Plan A's Efficacy (Situational Irony)
At the beginning of the film, Professor Brand insists that there are two plans to save humanity: Plan A, which is to get everyone off of Earth, or Plan B, which is to colonize the new planet with pre-fertilized eggs. However, Plan A is later revealed to be a massive lie designed to give everyone enough hope to carry out the space expedition. In the end, though, Plan A actually ends up being a viable solution once Murph solves the gravity equation, and so the irony is that what started out as false hope became genuine possibility, and indeed the answer to the film's major conflict.
Cooper Letting Go of the Hope of Seeing His Family Again (Situational Irony)
Cooper spends the majority of the space expedition determined to see his family again. However, once things look grim and he and Brand have to slingshot around Gargantua to reach Edmunds' planet, Cooper decides he will not continue on, instead choosing to let go of his hope of returning home. The irony is that only once he resigns himself to this fate is he able to find his way back through the tesseract and see Murph one last time. Had he remained determined to return home, he likely never would have.