Continuity mistake: When the three T-Birds go to moon at the TV camera at the National Dance Off, Doody says "1, 2, 3, go!" and pulls down his trousers to his ankles. In the next scene, his trousers are suddenly pulled right up to his buttocks.
Continuity mistake: At Frenchie's sleepover when they are talking about piercing Sandy's ears, it shows Sandy holding the wine bottle and passing it to Jan. Then it cuts back to Sandy and she is still holding the wine, then it cuts back to Jan and she has the wine again.
Continuity mistake: When "Crater Face" comes to the dance with Marty and Rizzo, he takes his sunglasses off twice.
Continuity mistake: In the scene where the whole gang is eating at the soda shop, everybody starts leaving. Doody is in the back, in the middle, on the railing. He's getting ready to leave, takes a bite of his ice cream and sets it down. In the next shot, he sets it down again.
Continuity mistake: In "We go together" they all dance forwards. When the camera changes angle Frenchy and Doody have switched sides.
Continuity mistake: When Marty is talking to Vince Fontaine before the dance contest, towards the end of their conversation she starts to lift up her purse with her right hand. But suddenly it cuts to another angle, and her arm is down.
Continuity mistake: Sandy walks over to meet the girls after doing a cartwheel. On Sandy's cheerleading uniform, there is a LONG red string right next to the letter on her shirt. Then, suddenly, the string disappears in the very next shot. Then in the scene after that it is back again, and then the string is back on her shirt. (00:22:20)
Continuity mistake: During the slumber party at Frenchie's, when Rizzo brings out the wine, check out the junk on the headboard. Later in the scene when Marty is putting on her robe, the headboard is clear and now has a black fan on the left. Then even later when Jan says "You ain't getting your hands on my ears" the headboard is cluttered again, with the black fan too. (00:27:35)
Continuity mistake: In the middle of the dance contest, Patty Simcox does a funny front walkover, and comes dancing towards the camera. Over her shoulder, you can see Sonny running up behind her. But suddenly it cuts to another angle, and Kenickie is running up behind her to lift up her dress, and Sonny is nowhere to be seen.
Continuity mistake: After Danny has danced around the car with the saran wrap he is shown spinning around numerous times, and then stops with his back to the camera. However, in the very next shot, his arms are suddenly up in a pose far too quickly for him to have done in the time alloted.
Continuity mistake: When Danny is first shown at school, he is speaking face-to-face with a girl in a blue sweater. The immediate next shot, Danny is talking to a totally different girl in a purple sweater, and he has his back turned from the camera.
Continuity mistake: During the car-racing scene, Danny's car has a big scratch in it. For the next few shots, it's missing and at the end of the scene, it reappears.
Continuity mistake: At the dance, when Frenchy insults Cha-Cha by saying, "With the worst reputation", Cha-Cha is shown (in the close-up) first looking at Kenickie, then turning her head around to give Frenchy a dirty look. In the next shot when Danny and Sandy are leaving the group, Cha-Cha is suddenly back at looking at Kenickie, then proceeds to give Frenchy the same dirty look again.
Continuity mistake: The TV set that is in the scene when Jan sings, "Brusha Brusha Brusha" is not the same TV that is shown when Rizzo is getting ready to go out the window during the slumber party.
Continuity mistake: After Danny has knocked over a hurdle, we see him getting up; however, the Hurdle has either moved and stood itself back up or it's disappeared completely. In the next shot it has returned to its fallen position.
Continuity mistake: When Patti gets her skirt lifted up at the dance contest, the two boys who were dancing on either side of her in the previous shot have both disappeared.
Continuity mistake: When Danny and Cha-Cha are dancing to 'Born to Hand Jive', watch the position of Principal McGee. During the song, you can see her in the crowd. A few shots later, she is now standing near the stage on her own, and when we return to Danny and Cha-Cha dancing, you can see the Principal back in the crowd again.
Continuity mistake: On the first day of school during lunch, at one point Frenchie has out a small compact and is checking for food in her teeth. But when it cuts to a wider angle, suddenly the compact is gone, and she's looking over her shoulder.
Continuity mistake: During the Greased Lightning song sequence, when Danny runs around the dream car, from one shot to the next, 2 white mattresses suddenly appear behind the car to aid the dancers jumping off. (00:39:55)
Continuity mistake: At the start of the Rydell fight song at the dance, Patty is standing right at the front of the stage. One second later, she is at the back of the gym.
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.
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.