Continuity mistake: As Tom Cruise walks to the Amtrak train with Dustin Hoffman near the end, they stop about 1 pace from the train door, but in the next shot the pair walk about seven paces to the same spot in front of the train door.
Continuity mistake: After the duo stops at a motel with pink neon, Ray starts reciting his riddle about the guy on first base again, which gets Charlie annoyed and he badgers him over it. After their little exchange, Ray is walking up to the side of the car as Charlie opens the door to their room. Ray is standing very close to the car, standing right on the yellow line of the parking space. The camera then suddenly jump cuts to a higher angle and Ray is now several feet back standing in the middle of the next parking space over.
Answer: It's "I Saw Her Standing There," written by John Lennon and Paul McCartney, released November 1963. In addition to the Beatles, the song has been covered by Elton John, The Grateful Dead, Tiffany, and many others I'm sure.
Matty Blast
In December 1963, Capitol Records released the song in the United States as the B-side on the label's first single by the Beatles, "I Want to Hold Your Hand."