It's the first film to win Wes Anderson an Oscar. Well four Oscars: Costume Design, Makeup and Hairstyling, Original Score and Production Design.
The Grand Budapest Hotel marks the 7th film Wes Anderson has made with Bill Murray.
Johnny Depp was set to be the lead, but he dropped out and Ralph Fiennes replaced him.
The whole cast and crew stayed at The Hotel Börse in Görlitz. They ate every meal together and Anderson brought an Italian cook to make them their meals. They changed costumes and did their make up in the lobby in order to gain more time for filming. (Source)
Apparently, Tony Revolori and Saoirse Ronan were told to "Go for it" by Anderson in a scene where they rip each other's clothes off. They had to do the scene several times, this made the costume designers furious. (Source)