Continuity mistake: In the cafeteria, when Mr. Strickland is glaring at Marty and Biff, the table Marty was sitting at with George is behind him. When Biff leaves there is a close-up of the table and both the lunch tray and Marty's jacket have changed positions significantly from the previous shots (George had already left). (01:00:30)
Continuity mistake: When Marty pulls the family picture from his shirt pocket in front of George's house, he holds it with both hands at first. But once the angle changes, only his right hand has a grip on the picture. (01:01:45)
Continuity mistake: When Marty is standing over his father's bed in 1955, Marty puts the headphones on George and then puts the tape in the cassette player. If you notice the hairdryer is on the left side of the belt and is touching his left arm, but when they cut to Marty holding the tape player out in front of him the hairdryer is on the right side. (01:02:10)
Continuity mistake: When George goes into the cafe to tell Lorraine he is her density/destiny, the people sitting at the bar keep changing with different shots. Best example is just after George refers to his "density" - in the background there's a brunette in a blue jumper at the bar. A blonde woman and a short-haired guy then sit on her left, but then disappear in the shot of Marty sitting at the bar - on the brunette's left there's now another brunette in a pink jumper with a different guy. The brunette's got shorter hair too. In the very next shot the blonde's back with no sign of Marty. (01:02:10)
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)
Revealing mistake: When Marty is being chased on the skateboard in 1955 he skids rounds a corner and you can see that this scene had been shot before as there are skid marks there from previous takes. (01:03:20)
Revealing mistake: 1955 skateboard chase scene around town square. Note in this scene a metal device has been added between the kicktail and the back truck of the skateboard to create the sparks, then disappears and reappears throughout the whole chase scene. (01:03:40)
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)
Factual error: When Biff is chasing Marty (on the 'skateboard') around the Town Square, you can see curb cuts at the corners. Aside from a trial program in Kalamazoo, Michigan in the '40s, they didn't spread further until well after 1955. (01:05:58)
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)
Revealing mistake: When Biff and his gang are chasing after Marty in their car around the Courthouse Square, in the shots that takes place in the Courthouse yard, you can see that it's Biff's stunt double that's driving. (01:06:45)
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