Revealing mistake: When Sandy is at the shop with the jock, then she goes to the jukebox, the picture behind the jock is all blurred out. You can tell it is a Coke sign - Coca Cola cancelled their sponsorship after filming. (00:43:30)
Revealing mistake: In the soda shop, the waitress turns off the lights with her elbow because her hands are full, but she misses the light switch by 6 inches. (00:55:10)
Revealing mistake: At the dance, there's a scene where everyone started dancing after Cha-Cha and Danny won the trophy. Well Marty comes in from the side of the screen and lands on the floor in some kind of split, and you can see she is wearing a knee pad on her right knee.
Revealing mistake: When Sandy checks into school for the first time, she goes down to the office and the assistant principal gives her some forms to fill out. If you look closely, you'll be able to see that the top form is just a blank piece of paper.
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