Inheritance
The film begins with the very wealthy Madame D. passing away and leaving an incredibly large fortune to be distributed among her family and Monsieur Gustave, her lover and closest confidant. Inheritance then becomes a major theme, as Dmitri and his three sisters believe they have a right to their mother's fortune, in spite of treating her poorly (and ultimately, murdering her). When Gustave is left a priceless painting, they try to frame him for murder in order to acquire it. Thus, the theme of inheritance sets into motion the entire plot of the film. By the end, we learn that Madame D. had an inkling that she would be murdered, and that her killer would be her son, and has thus made provisions that in the event she is murdered, Dmitri's inheritance will go completely to Gustave. The happy ending is that Gustave inherits Madame D.'s fortune, and Zero inherits that from Gustave.
Class and Civilized Society
The theme of class and modern society is a large part of the film. All of the guests at the Grand Budapest Hotel are very wealthy, and the employees of the establishment are meant to serve their needs at any cost. Gustave takes immense pride in his ability to bring his guests what they need with zeal and grace, and this pride is rooted in his well-mannered air and classy comportment.
Stories
This film is based on a story by an author who himself heard a story from Mr. Moustafa, the once owner of the Grand Budapest Hotel. The film thus has two "frame stories" encapsulating the narrative, and seems to be interested in the nature of storytelling itself. Much of the information is secondhand and filtered through multiple people's accounts of the event, which could perhaps explain the whimsicality of the film, and its more surrealistic elements.
Stories are recycled and passed down, and they have the ability affect the next generation. This is represented by the young girl at the opening and closing of the film coming to the statue of the "Author," who wrote a book called The Grand Budapest Hotel based on the story he was told by Mr. Moustafa. Stories get passed down inter-generationally and have the power to impact people years in the future.
Money & Corruption
While the high society of the Grand Budapest Hotel is based in money, the film makes a distinction between money-grubbing and a more nuanced appreciation of the finer things. While Gustave celebrates the value of his possessions, and cherishes the props and privileges of the upper classes, Dmitri is a murderous and corruptible cash-monger, and his desire for wealth pushes him to violent ends. Thus the corruptive power of money is a major theme in the film.
Throughout the film, Dmitri believes he lives outside the law because of his money. He kills his own mother, then hires an assassin to intimidate others into giving him money that is not rightfully his. In this way, his dirty antics are in direct contrast to Gustave's honest ways.
War and Refugees
In a broader sense, this film deals with war and refugees, as Zero is a victim of a war-torn country and has found himself displaced by the imperial forces that have brought about the decadence of places like the Grand Budapest. At one point, Gustave gets very angry at Zero when Zero neglects to bring Gustave's cologne, denigrating Zero's country of origin and asking why Zero felt entitled to come to Europe. Gustave is put in his place when Zero informs him that he had no choice, that he came to Europe as a result of a barbaric war going on in his own country. Zero is a refugee, the direct victim of the violence of war.
War catches up to him in Europe, and in the latter half of the film, Gustave and Zero are not only contending with Madame D.'s murderous children, but also the arrival of military troops in the region.
Loyalty
Gustave grills Zero when he first meets him, and wants to make sure that he is well-suited for the job of lobby boy. In the role of lobby boy, Zero must prove his undying loyalty to the Grand Budapest Hotel and to Gustave as his superior. When Zero passes Gustave's tests, he is rewarded in kind with Gustave's unfaltering loyalty. The bond of trust between the concierge and his protege is profound, and they stick together throughout many hardships. Gustave's ultimate act of loyalty comes at the end, when he dies at the hands of the fascist soldiers in order to save Zero's life. While Gustave seems like a rather superficial character, he is, in fact, a man of integrity, and he is willing to put himself on the line on behalf of his young friend.
Romance
A lesser theme in the film is love. While Gustave's relationship with Madame D. is primarily carnal in nature, there is also an actual love shared between them, and she feels more loving and trusting towards him than towards her own children. Promiscuous though he may be, Gustave is capable of deep affection and love, and does not shy away from expressing his more romantic affiliations, particularly through his recitation of romantic poetry.
Agatha and Zero also share a profound love between them. They kiss passionately at the movie theater, proposing to one another and professing their romantic attachment. Their love binds them together through the ensuing caper, but is tragically cut short by Agatha's death. Even after her unfortunate expiration, however, Zero continues to honor her memory, and tells the Author that he purchased the Grand Budapest Hotel in her honor. Love is an important theme in an otherwise farcical and whacky film.