SPOILER: There are two scenes set after the closing credits. The film's main post-credits scene is of the Deadpool, still alive after being decapitated, reaching for his head, leading into Deadpool (2016). An alternate post-credits scene seen (only on the DVD) is of Wolverine in a Japanese bar, leading into The Wolverine (2013). During the original theatrical run, which scene you saw was random depending on your theater; the home video version features the Deadpool scene after the credits and the Japanese bar scene is available on the two-disc DVD as a deleted scene.
For the X-Men trilogy, when the 20th Century Fox logo fades away, the 'X' in the logo stays for a second longer before it also fades away. For this film, the 'X' disappears with the rest of the word.
This is the first X-Film to have an opening credits sequence: Logan and Creed fight together through a montage of wars: the American Civil War, WWI, WWII, and the Vietnam War.
SPOILER: There is a scene in the closing credits: William Stryker is arrested and taken into custody for the murder of General Munson).