Visible crew/equipment: In a scene in the principal's office reflections of the crew can be seen in the bookcase glass. A crewmember wearing headphones and holding the boom can be seen fairly clearly.
Visible crew/equipment: When Danny is talking to Cameron just before Derek enters the room, look at the map of the United States on the wall right behind where Danny is sitting. There is a visible reflection of a stage light. There are several other lamps in the room as part of the make up of the room, but due to the size and intensity of this reflection, it's quite obviously from a stage light.
Visible crew/equipment: Before the killing of the black guy happens, in the scene where Derek is arguing with the English Teacher (Murray) about civil rights, he hurts Jennifer Lien. He then takes off his shirt and shows Murray the German Swastika on his chest, as he does this you can easily see some of the undressed studio set behind him as instead of a ceiling there is simply a black wall at the top.
Visible crew/equipment: When Cameron is talking to Derek in his office and says "You're on safe ground.", tripods, stage lights, and set parts are reflected in his glasses. (01:02:20)
Visible crew/equipment: During Derek's "I am out" declaration to Cameron, the cameraman's reflection is visible in the framed photo twice, as they argue/fight.
Visible crew/equipment: When Sweeney and Murray are debating about how to handle Danny after the stunt he played in class, look closely at the bookcase behind Sweeney. You will notice a reflection of an object, likely a piece of equipment, hovering up and down above Sweeney's head. While it is difficult to make out what this object is, it is definitely something that would not ordinarily be there.
Visible crew/equipment: When Derek is in prison speaking to Doris (his mother) whenever the camera is facing Derek you can see the reflection of the camera in the glass.
Visible crew/equipment: When Derek is entering the party with Seth you can actually see the shadow of the camera and of some crew members on Derek's and Seth's bodies. It just takes a sec, but I think it's clear.
Visible crew/equipment: When Derek comforts Danny in the bathroom after he has been shot, we see a shot of the detective. If you look behind him you can make out a pole of a boom mic. It isn't clear as the background is slightly blurry, but it's there. (01:53:45)
Visible crew/equipment: When Derek is running into the bathroom after Danny has been shot, as he is running through the crowd of students, it cuts to a shot from the side of the hallway, it's very quick, but you can see a camera, a cameraman, and the boom mike and its operator.
Answer: The tattooed DOC on gang members' arms means Disciples of Christ - the gang that they belong to in the movie.