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.
The story is set in 1965, yet it shows many modern (as of filming in 1983) pieces of medical equipment, such as disposal plastic nasal cannula, modern plastic IV tubing and cut offs, etc. Also most hospitals in the 1960s had open wards with many patients cordoned off by curtains, instead of private rooms as depicted in the movie.
The movie is set in 1965. However, when Dallas is reading the magazine, just before he robs the convenience store, comic books from DC Comics and Charlton Comics are shown with logos that were introduced in 1977 and 1973 respectively. Also, one of the titles shown (Captain Carrot and the Zoo Crew) was based on characters who were first introduced in 1982.
When Dally, Johnny and Ponyboy are watching the movie at the drive in, Ponyboy starts laughing, but in the next shot we see Ponyboy in the background not laughing while the audio track of his laughing is still continuing (at 07:23 to 07:25 in 91 m.).
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 (at 01:05:33 in 91 m.). In the next shot, he is reaching with his right hand (at around 1h 05 mins).
During the Rumble, when all the Greasers are lined up, Ponyboy is on Darry's right (at 01:13:35 in 91 m.), but when Darry turns to Ponyboy to tell him to stay close, Ponyboy is on Darry's left (at around 1h 14 mins).
In the scene where Ponyboy is reading the letter from Sodapop, Dally is seen in the background with his right thumb hooked in his pants pocket (43:31 to 43:38 in 91 m.). The shot switches to a close-up of Dally lighting his cigarette with just his left hand while his right hand is about chest high (43:39 to 43:42). Then the camera comes back to Ponyboy with Dally in the background with his right thumb hooked in his pants pocket (43:43 to 43:45).
At, the very end, when Dally robs the bank, he pulls out his gun at the store clerk and he points it on the clerk's right cheek (at 01:23:27 in 91 m.). The next shot of the clerk, shows the gun on the left side of the clerk's cheek (at around 1h 23 mins).
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 (at 24:50 in 91 m.). In the next shot that he takes out his blade the hole is gone (at around 51 mins).
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. (The 91 minute version does not show how they first get into the church.)
Just before the Socs attack Ponyboy, he taunts them (in retaliation to their comments) by saying, "You know what a Soc is? White trash with Mustangs and Madras". The subtitle reads, "You know what a Soc is? White trash with Mustangs to match". ("Madras" is a lightweight fabric used for summer wear, so he is referring to their "classy" outfits in comparison to the Greasers' T-shirts and jeans).
Dallas falling out of the chair at the Drive-in (at 07:18 in 91 m.) was an accident and was not rehearsed. Ponyboy looks at the camera expecting Francis Ford Coppola to say cut, but they kept the shot instead.
After the boys come over for breakfast near the end of the movie, Ponyboy goes out on the porch. When he goes out (at 55:13 in 91 m.) there is a rip in the screen in door. When he comes back in the rip is gone (at around 26 mins). This is because the screen is pulled away from the frame near the door handle which can be seen when the door is open (55:13), but not when the door is closed (55:26).
The goof items below may give away important plot points.
When Johnny and Pony boy go see Dallas at the bar after Johnny kills the Soc, there's a song called 'Loveless Motel' by R.C Bannon that's playing on the jukebox. That song wasn't recorded until years after the movie actually takes place.
Bob moves his head and arm when he's supposed to be dead. It happens in the background during a closeup on Johnny's face, right after Johnny says "They all ran off. I stabbed 'em. They all ran." (28:30 to 28:37 in 91 m.) [If he moves in the 91 minute version, it's slight and not obvious.]