Continuity mistake: Rizzo is singing the Sandra-Dee song in Frenchie's bedroom. When she sits at the desk, you can just see that the chest of drawers are all closed fully behind her. However, later in the song Rizzo jumps off the bed. As she passes, then sits back at the desk, the second drawer down is now partially open. No one goes near it during this time, as all the girls in this song are on the bed.
Continuity mistake: During the sleepover, Rizzo gets off of the bed with a cigarette in one hand and the wine bottle in the other. In the next shot, the cigarette and the bottle have switched places.
Continuity mistake: After Vince Fontaine begins the National Dance Off with Johnny Casino & The Gamblers, Mr. Rudie is seen walking down some steps near the stage, but in the very next shot he is seen at the bottom of the steps, putting his hands up to Vince.
Continuity mistake: In the song "There Are Worse Things I Could Do," between the lines "Out of spite or jealousy" and "I don't steal and I don't lie", Rizzo's hand jumps from the side of her book to the top of her book, near her face.
Continuity mistake: During the dance, there's one song where the guys stand in one line and the girls in another, and the couples take turns walking down the middle. In one shot, Danny is placing Sandy in line, and a couple (the woman has a blue dress on) is already starting down the middle. Then it cuts to another angle and no one is in the middle. Back to the first angle, and people are in the middle again.
Continuity mistake: When Principal McGee does her announcement to all the students at the beginning of the film, you can see a flag of the United States at the far end of her desk, but when we see a close-up of the Principal, the flag is now right in front of her.
Continuity mistake: In the scene where the whole gang meets at the diner, the waitress brings out Danny and Sandy's food, and you can see the drinks they have ordered are a dark pink colour. In the next shot that they appear, the drinks are a lot lighter shade, almost pale pink.
Continuity mistake: When Marty and Rizzo walk past the TV truck, Marty says "Rizz!" and they stop and look at Kenickie, whose head is tilted to the right, but in the next scene his head has moved to the left.
Continuity mistake: When the three T-Birds go to moon at the TV camera during the performance of "Blue Moon" at the National Dance Off, you can see there are two red balloons in front of Doody, but in the next shot the balloons have disappeared.
Continuity mistake: When Sandy is asking Rizzo if she's going to Thunder Road, her hair is curled under. When she's watching the race and then talking to Frenchy after Danny wins, her hair is flipped outwards.
Continuity mistake: During the basketball lesson with the team and Danny, Coach Calhoun is holding the ball and tells him, "You have to dribble." At this point you can see that Danny is very close to the coach, but in the next shot he is further away from him.
Continuity mistake: During the dance contest, when Kenickie and Cha-Cha are dancing around like crazy (when she puts her foot up on his shoulder), you can see Danny and Sandy in the background, standing on the sidelines. Given that they're the last couple on the floor at the end, they should still be out dancing at this point.
Continuity mistake: When Sonny enters the sports hall for the National Dance Off, he twangs Chisum's braces and walks towards the bandstand. Chisum is well away from the doorway at this point. However, in the next scene, Chisum is now standing near the doorway and Sonny is walking away from the bandstand.
Continuity mistake: Widescreen version: When Vince Fontaine introduces Johnny Casino & The Gamblers at the National Bandstand, Blanche is seen walking off the stage. In the next scene, she is on the stage, dancing with the band.
Continuity mistake: At the dance when they do that partner dance down the middle of the gym, as the lines form Kenickie and Cha-Cha start dancing down it, then the next shot its another couple first down it, and then a couple of shots later Kenickie and Cha-Cha start going down the lines again.
Continuity mistake: When Danny is running on the athletics track, he falls over one of the hurdles. He then picks him up and Sandy goes over to see if he is okay. You can see that Danny is walking towards to the field section of the track, but in the next shot he is walking away from Sandy.
Continuity mistake: When Jan is eating her lunch, she is joined by Marty and Rizzo. Jan then says "Did you guys get a look at Zuko this morning?" and you can see she has nothing in her right hand, but in the next shot she is holding a fork.
Continuity mistake: During the race at Thunder Road, look at the length of the wheel cutters - they keep changing length throughout the whole race. Plus we only see one come off, but before the crash the two Westside ones are missing.
Continuity mistake: When Danny and Sandy enter the sports hall for the National Dance Off, there are four people behind them sitting on the spectator benches, but when Doody and Frenchy enter the hall in the next shot, the people have disappeared and there is now a woman in a pink dress behind the benches.
Continuity mistake: The scene where Sandy and Danny are eating together, then the rest of the gang comes, Sonny walks Marty home. Right after the two leave, Sonny come up behind Frenchie, like he was in the bathroom or at the jukebox. Wasn't he walking Marty home?
Answer: Well, Danny was out of town, at the beach. It's quite possible that the rest of T-Birds didn't live close enough to each other to see each other during the summer. Also, they may have all had jobs, or been travelling with their families. It's also possible that they DID see each other, although maybe not as "T-Birds". When they saw each other on the first day of school, though, they were Seniors, and they were ready and excited to be T-Bird seniors.
BGraz
Another possible reason is that not all of them were allowed to see friends during the summer. I had a couple of classmates whose parents were strict about them focusing on schoolwork and/or getting a job. No phone calls or visiting friends on the weekends or during summer: "You can see your friends at school."
Do you really think any of the T-Birds had strict parents?
People quite often rebel against strict parents.
When they asked Kenickie where he was, he said "working, which is more than I can say for any of youse kids" suggesting that the 3 stooges (pun intended for their stupid routine that prompts Danny to tell them to "be cool") didn't work all summer. Also, Sonny needed to borrow money in the dinner until he could get his allowance.
In regards to not living close enough to each other, it is worth mentioning that having access to a vehicle was much less common compared to nowadays.
KeyZOid