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)
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)
Continuity mistake: When Biff and gang are chasing Marty on the skateboard, they eventually crash into the rear of a manure-hauling dump truck. When the car swerves left in an attempt to miss it, it will obviously pull somewhat to the left. In the shot just before impact, you can see that just the rear half of the car should impact the truck, but in the next shot the car rests perfectly centered behind the dumps open load. (01:07:25)
Continuity mistake: After Goldie Wilson arrives at the manure truck scene, we can see onlookers approaching at the street corner in front of Texaco - one of which is the kid who Marty borrowed a skateboard from. But once the shot changes, that same kid is instantly standing on the sidewalk near Marty holding a crate instead. (01:07:35)
Continuity mistake: When Biff and his friends are chasing Marty on the skateboard, just before they hit the manure truck there is canvas covering the fertilizer which disappears in the next shot. (01:07:45)
Factual error: In the skateboard chase scene, after the crash, a crowd gathers. In this crowd there is a kid dressed in a Cub Scout uniform. He has a red/white town strip patch on his arm. In 1955 the Cub Scout town strip patches were blue with gold lettering. (01:07:48)
Continuity mistake: Whilst George McFly is pegging out the laundry, Marty is explaining his plan as to how he can make Lorraine fall in love with him. At the start of the scene, both of Marty's breast pocket flaps are untucked. After putting the bag down, one tucks itself in, then they return to normal when Marty says "let's go over the plan again". (01:09:55)
Audio problem: Lorraine comes to see Marty in Doc's garage in 1955 to ask him if he will go to the dance with her. Just before Lorraine moves to the other side of the car from where she walked in, she begins to say something to Marty. The problem is that her lips don't move when she talks, I guess the right clip ended up on the editing room floor. (01:11:40)
Continuity mistake: In the scene where Marty tells George his plan for getting Lorraine to go to the dance with him, Marty's shirt is sometimes tucked in and sometimes not. (01:12:40)
Continuity mistake: When Marty takes a swig from the bottle, we see the motion of Lorraine's hands as she lights a cigarette. She finishes lighting and then grabs it with her left hand. In the next shot where Marty spits alcohol all over the place, Lorraine is busy lighting her cigarette a second time. (01:18:10)
Continuity mistake: When George is checking the time at the prom there is a girl in grey behind him that changes to one in pink. (01:18:56)
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