Dr. Emmett Brown: This sucker's electrical. But I need a nuclear reaction to generate the 1.21 gigawatts of electricity I need.
Marty McFly: Doc, you don't just walk into a store and buy plutonium. Did you rip that off?
Dr. Emmett Brown: Shhhhhh. Of course. From a group of Libyan nationalists. They wanted me to build them a bomb, so I took their plutonium and in turn, gave them a shiny bomb-casing full of used pinball machine parts!
[Doc is wearing his thought reading device.]
Marty McFly: Doc, I'm from the future. I came here in a time machine that you invented. Now, I need your help to get back to the year 1985.
Dr. Emmett Brown: My god. Do you know this means? It means that this damn thing doesn't work at all!
Dr. Emmett Brown: Well, they're your parents you must know them. What are their common interests? What do they like to do together?
Marty McFly: Nothing.
Dr. Emmett Brown: No wonder your president has to be an actor, he's gotta look good on television.
Sam Baines: Stella! Another one of these damn kids jumped in front of my car! Come on out here and help me take him in the house!
Marvin Berry: Chuck. Chuck! It's Marvin - your cousin, Marvin BERRY. You know that new sound you're looking for? Well, listen to this!
Dr. Emmett Brown: Now, remember - according to my theory, you interfered with your parents first meeting. If they don't meet, they won't fall in love, they won't get married and they won't have kids. That's why your older brother's disappearing from that photograph. Your sister will follow, and unless you repair the damage, you'll be next.
Marty McFly: Sounds pretty heavy.
Dr. Emmett Brown: Weight has nothing to do with it.
Biff Tannen: Why don't you make like a tree and get out of here!
Marty McFly: Silence, earthling! My name is Darth Vader. I'm an extra-terrestrial from the planet Vulcan!
[Lorraine's parents are talking about Marty McFly, Lorraine's future son.]
Stella Baines: He's a very strange young man.
Sam Baines: He's an idiot. Comes from upbringing. His parents are probably idiots too. Lorraine, if you ever have a kid that acts that way I'll disown you.
Marty McFly: Jesus, George, it was a wonder I was even born.
Doc: Next Saturday night, we're sending you Back to the Future!
Biff: Why don't you make like a tree, and get out of here?
Lou: You gonna order something, kid?
Marty McFly: Ah, yeah... Give me a Tab.
Lou: Tab? I can't give you a tab unless you order something.
Marty McFly: All right, give me a Pepsi Free.
Lou: You want a Pepsi, pal, you're gonna pay for it.
Answer: The video camera was in the DeLorean. With the right kind of adapter, which was common enough in the 80s that Doc might've had it on the camera or been able to jury-rig something in the 50s, it would have been possible to connect it into the antenna screws in the back of the TV like an old Atari and play it directly from the camera.
Captain Defenestrator
TVs in the 50s had a two prong antennae connection (two screws in the back that you put a prong antennae into) TVs in the mid 80s also had this. The coax connection (the one wire that screws in) was starting to become common, but, the two prong connection would have been more likely on any given TV at the time, so, whatever wire they used to preview recordings probably had that. very convenient that Marty brought those cords with him.
An old Atari 2600 RF Adapter would be how one would link a video camera to an old-fashioned television. A simple-enough part that Doc could probably make one with 1950s technology.
Captain Defenestrator