Continuity: When the boys arrive at the church fire, Johnny opens his door on the passenger side of the convertible twice.
Anachronisms: When Ponyboy and Johnny go to the bar to see Dally, there is a song playing on the juke box called 'Jack Daniels if you please' by David Allan Coe, this song was written and released in 1978 although the movie takes place in the 1966.
Continuity: During the rumble, the Greasers and Socs are alternately wet/dry between shots, and the mud on Paul's white pants appears, and disappears, etc.
Continuity: Johnny's newspaper photo has him with short hair, but he didn't have his hair cut until just before the fire- from which he got severe burns. In his photo he is fresh faced.
Continuity: Dally rolls the window down to talk to the policeman, but when the policeman goes in front to escort him, the window is suddenly up and is instantly fogged up again.
Continuity: Randy is leaning on the car as he talks to Ponyboy, but in the close-up view only his arm is leaning on the car.
Anachronisms: When Dally uses phone, a tilted In-and-Out burger cup is visible. There were fewer than 20 open at the time, and only in Southern California.
Continuity: The bruise around Dally's right eye varies in size between shots after the rumble and into the hospital.
Audio/visual unsynchronized: When Dally, Johnny and Ponyboy are watching the movie at the drive in, Ponyboy starts laughing, but in the next shot we see a background shot of Ponyboy not laughing while the audio track of his laughing is still continuing
Incorrectly regarded as goofs: Dallas falling out of the chair at the Drive-in was an accident and was not rehearsed. Ponyboy (C. Thomas Howell) looks at the camera expecting Francis Ford Coppola to say cut, but they kept the shot instead.
Continuity: When Ponyboy is standing in front of the bathroom mirror, he is wiping his face with a towel. In the next shot where Sodapop comes out of the shower, you see Ponyboy standing in front of the mirror combing his hair.
Continuity: When Dally is in the hospital on his bed, he asks for a pocket knife. In the first shot he is reaching with his left hand while his right hand is under the blanket. In the next shot, he is reaching with his right hand.
Continuity: When Johnny and Ponyboy are at the park, and the Socs first get there, Johnny reaches for his blade, in that shot Johnny's jeans have a hole on the pocket. In the next shot that he takes out his blade the hole is gone.
Continuity: When the boys are breaking into the church there is some glass still attached to the sides of the window. They knock down some of it from the top, but some on the sides and top is still there. It disappears when they go through.
Anachronisms: After the boys come over for breakfast near the end of the movie, Ponyboy goes out on the porch. When he goes out there is a rip in the screen in door. When he comes back in the rip is gone.
Continuity: When the Soc's chase after Ponyboy and Johnny after he spits in Bobs face, there is a duck in the fountain in one shot, and then the next it's gone.
Source: IMDb.com