Moustafa sleeps in his old room (Situational Irony)
When the Author arrives at the Grand Budapest, he is surprised to learn the Mr. Moustafa, the wealthiest man in the country and the owner of the hotel, sleeps in a tiny staff room in the back of the hotel. As he comes to find out, this is the room that Moustafa stayed in when he was only a small and powerless lobby boy. Moustafa's decision to live in the past, in spite of being such a wealthy and powerful man, is ironic in its unexpectedness.
The Newspaper Headline (Situational Irony)
Early on in the movie, Zero gasps at a newspaper headline unseen by the viewer, and runs to show Gustave. When the camera does finally reveal the paper, we see a headline about the fact that a war is breaking out. Given the dramatic stakes of war, the viewer assumes that this is the headline that made Zero gasp, but the camera pans down moments later to reveal a headline about the fact that Madame D. died. This is ironic both because of the way that Wes Anderson shoots it, in that it subverts our expectation by panning from one headline to another, and because, in the grand scheme, war is far more alarming than the death of a woman in her 80s.
Replacing the painting with a famous painting (Dramatic & Situational Irony)
Boy with Apple is a fictional painting, but we are told that it is priceless and very famous, perhaps the most valuable of all of the countess' possessions. When Gustave and Zero go to steal it, they simply take it off the wall and replace with a painting that is sitting around nearby. The painting sitting nearby is a painting by the renowned real-life painter Egon Schiele. It is called Two Women, it is from 1915, and given Schiele's fame, it is likely worth a great deal of money. Thus, there is an irony in the fact that Gustave and Zero do not recognize it, and decide to take the fictional painting instead. This is also an instance of dramatic irony, because while the viewer who is well-versed in art history would recognize the Egon Schiele, Gustave and Zero are clueless, and do not treat it with any kind of reverence.
Gustave does well in prison (Situational Irony)
Given his effeminacy, bisexuality, and general finesse, Gustave does not seem like he will fare very well in the rough cell block of prison. Indeed, when he comes to talk to Zero during visitation hours, he is considerably roughed up and Zero suspects that he is having a tough time. However, Gustave explains that he has proven himself in prison, has gotten in his share of fights, and is integrating easily with his violent surroundings. While nothing about his affect has changed—he is still as dainty as ever—he is well-versed in prison slang, and in this regard, makes a convincing inmate. Thus there is an ironic tension between the fact that Gustave is such a cultured and gentle creature, but he can also hold his own with some violent criminals.