Other mistake: On the first day of school, when Patty is starting to sit down next to Sandy, her reaction to sitting on the apple is way too early.
Other mistake: This mistake occurs during the dance sequence 'You're the One that I Want.' John Travolta and Olivia Newton-John have just emerged from a 'Shake Shack' and are now ascending a ramp. For the lyrics ,Hoo hoo hoo... honey,' the camera zooms in close to their faces. You can see that the dance move is for the two actors to bob their heads close to each other's so that they nearly touch. They do it right the first time, but the second time they visibly mess up. John Travolta seems to try to fix his mistake, but Olivia Newton-John appears to crack up and leave the frame.
Other mistake: The entire "Greased Lightning" number repeatedly goes in and out of focus.
Other mistake: At the dance, students are still arriving as the band starts to set up. A moment later, the MC announces over the mic that Johnny Casino and the Gamblers will get things warmed up, and then music starts, which is not possible with the band just setting up.
Other mistake: In the opening animated sequence, it shows Rizzo taking off a top and her neck stretching. She looks in the mirror. As she is facing the mirror you can see that even with the elongated neck you still should be able to see her face in the mirror, but the elongated reflection just shows the neck looking much longer than it really should. Also, as the animation goes on you see Riz turning sideways but the reflection in the mirror does not match. She is sideways while her boobs in the reflection are facing the other direction. Then when she puts the black blouse on her back is to the mirror but we see her front in the mirror.
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