Visible crew/equipment: In the soda shop scene where Sandy and Danny are at the jukebox, the reflection of the boom mic is clearly visible in the chrome part of the jukebox. [True of videos and early DVD releases - in later DVD releases the reflection has been removed].
Visible crew/equipment: In the scene during the American bandstand, at the end of the song when the teacher is dancing in front of the band members, the crews can be seen. The dressing and the hair doesn't match Grease era at all, and someone is sitting on a director's chair as well. (01:06:20)
Visible crew/equipment: In the scene where they are singing Grease Lighting - the part when the fuzzy dice float to Kenickie - after he takes them "out of the air" and swings them around, then lets them fly - if you look close to his head you can see the white string they were attached to when they were "floating".
Visible crew/equipment: When Danny is about to play basketball with the other students and Coach Calhoun is speaking to him, you can see the shadow of the boom mic behind the coach.
Visible crew/equipment: When Sonny snaps Tom's suspenders as he enters the gym, you can see a microphone in the top right corner.
Answer: Watched that scene again now and I just think it was poor writing (in what's still a classic film regardless). How none of the judges noticed that Cha Cha took another girl's (Sandy's) place even after she'd already been "tapped out" is another huge plot hole. Plus a lot of people in America were watching the dance on TV and it's not mentioned by anyone after this scene. 35 years later and that scene still bugs me (haha).