Continuity mistake: When Marty confronts George as "Darth Vader", after George asks "who are you?" Marty plays the music again, and George presses his hands to his ears. In the shot from behind, his hands are cupped around his ears, in a very different position. Then when Marty says "silence earthling", in the shot from the front his hand is away from his ear entirely. (01:02:35)
Continuity mistake: When George and Marty are talking outside the diner and George opens Marty's coke bottle for him, George's hair is all stringy and hanging down in his face. But when it cuts to another angle, it's neatly combed over to one side. (01:03:10)
Continuity mistake: In the 1955 skateboard chase scene around the town square, note how the skateboard used throughout the whole chase scene changes at least 4 times. Namely different wheels, trucks and the trucks' wooden mountings. (01:03:15)
Continuity mistake: When Marty is being chased on the scooter turned skateboard, he is hanging onto the corner of a blue truck. Biff tries to smash him between the two, and the camera shows him pulling himself along the side of the blue truck, then hanging off the back corner again. (01:04:10)
Continuity mistake: In the escape from Biff on the skateboard, Marty collides with a couple near some steps. His skateboard is left at their feet, but after a cut his skateboard's now behind the woman's head in an ideal place for Marty to grab it. The papers thrown in the air suddenly multiply and appear on the ground (under the people, which means they must have dropped the papers first before falling over!). (01:04:15)
Continuity mistake: 1955 Skateboard Chase Scene around Town square. After Marty falls over the couple, a shot of Biff's car shows all the passengers standing up, but in the very next frame everyone is sat down. Also, that is not Biff driving. (01:04:20)
Continuity mistake: 1955 Skateboard Chase Scene around Town square. Throughout the whole chase scene two visible different stunt drivers are used to drive the two different models of Biffs' Ford. One is a 1946, the other is a 1947. Note the different position and shape of the front turn sign. (01:04:25)
Continuity mistake: When young George walks to Lorraine's table to read the poetic lines, the pen in front of her books moves suddenly to being on the right side of the books. (01:04:42)
Continuity mistake: After Marty borrows the improvised skateboard from the boy, in the first close-up of his feet his tied looped laces are extremely short, but when he climbs over Biff's moving car and then lands on the skateboard, the length of his tied looped laces is significantly longer. It shortens again thereafter. (01:06:05)
Continuity mistake: When Marty rides off after borrowing the skateboard, a woman in the background bends over towards the end of the shot, but in the next shot, she is standing upright. (01:06:10)
Continuity mistake: When Marty is on a skateboard being chased around the town square by Biff and his friends, he grabs the back end of a truck. After the truck makes a right turn, notice how the two kids he initially stopped to get a skateboard from at the beginning of the scene suddenly appear standing at the street corner between shots, holding their wooden crates. (01:06:25)
Continuity mistake: When Biff chases Marty out of the cafe in 1955 and Marty 'makes' the skateboard, there is an odd shot of a tree. When Biff's car drives through the grass, the big tree in the shot is shaking violently, yet all the trees are completely still during the chase before and after this shot. During this entire scene, differences regarding varying degrees of windy then calm, wet vs dry pavement and variations in shadows cast are numerous. (01:06:30)
Continuity mistake: When Marty McFly is being chased around the town square by Biff and his buddies in the black convertible, an extra set of lights appear under the headlights on the car (goes from a 1946 Ford to a '47/'48). (01:06:45)
Continuity mistake: When Biff and his goon friends are in Biff's car, as they chase Marty on his borrowed 'skateboard', the car's rearview mirror repeatedly disappears and reappears, and the side mirror changes from round to square repeatedly. (01:06:50)
Continuity mistake: When Marty chases after Biff on the borrowed 'skateboard', Marty is wearing a dark grey belt and a red/blue print shirt under his red/beige jacket. However, when Marty is hanging on to the front of Biff's car as they turn a corner (and in another shot), Marty (stunt double) is wearing a light brown belt and solid tan shirt. (01:07:00)
Continuity mistake: When Marty looks at the car he is about to crash into, there is no one standing on the pavement, but when he jumps onto it, a man appears. There was not enough time for him to appear. (01:07:00)
Continuity mistake: When Marty approaches the couple, the couple goes down a step twice. (01:07:03)
Continuity mistake: After Marty wipes out in front of the town hall, he clutches the hood ornament on Biff's Ford. As the car turns, Marty moves himself towards the fender, but between shots he repositions and is now clutching the hood ornament like before. (01:07:05)
Continuity mistake: When Marty skates off after knocking over the couple, the car behind him is red and cream, but in the next shot, it turns completely red. A yellow car also appears in the second shot, when it was not present in the first. (01:07:10)
Continuity mistake: When Biff's car slams into the manure truck, in the first shot the side of the truck is adjacent to the car's back passenger door, but in the next overhead shot the side of the truck is adjacent to the front windshield. (01:07:20)
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