Continuity mistake: When Michael J Fox's parent kiss and the family picture (with everyone standing on the grass) gets fixed, Michael places the photo on the guitar, gets very happy and starts playing the guitar enthusiastically. Seconds later, a brief shot of the guitar shows the picture with Marty only, his brothers are missing. (01:26:18)
Continuity mistake: During dinner, when old-Lorraine says "We all make mistakes in life, children", she swaps from having one hand on the glass to both hands, between one frame and the other. (00:15:06)
Continuity mistake: When the clock tower tolls at 10:00, Marty rushes to the DeLorean and as he drives off there are two huge cable spindles at the curb's red edge, near the cloth (lying on the street) that covered the DeLorean. In the next overhead shot, with Doc Brown on the ledge, the cable spindles are gone down below. (01:35:50)
Continuity mistake: Right when the movie begins, a machine opens a dog food can and then pours it in the dog's bowl. When pouring the food, the can isn't moved around at all, but after the food drops, the label is missing a piece. (00:02:25)
Continuity mistake: When the JVC recorder is first played, the screen on the TV is a blue colour. Later, when Doc is playing the Libyan part again and again, the screen seems to be a brownish colour. (00:50:10 - 01:05:40)
Continuity mistake: After the scene where Marty and his band are rejected from the school tryouts, Jennifer and Marty are sitting down and a lady comes by and asks them for change to save the clock tower. After they attempt a kiss, Jennifer's dad calls for her from the car. In the background, an African-American man is standing looking in the window of a building, and then walking right. In the next shot, he has moved all the way to the left and is walking right. (00:10:30)
Continuity mistake: When Marty is using the phone to call Doc while he is in the diner, his watch (which is on his left arm) starts beeping and the guy behind the counter gives him a strange look. Marty rips out the phone book page and asks the guy behind the counter where XXX Riverside Drive is. Marty is no longer wearing the watch which he just had on seconds earlier. (00:37:55)
Continuity mistake: After the dance, when Marty arrives at the clock tower in Doc's car (across the street from the DeLorean), he parks precisely midway between the two stores. As the clock tolls, Marty jumps into the DeLorean, and in the overhead shot as Marty drives off, Doc's car is directly in front of the store with the blue awning. (01:31:20 - 01:36:00)
Continuity mistake: When Doc points out that Einstein's watch is in sync with his, the LED display changes from being off in a wide shot to on in the closeup. (00:20:05)
Revealing mistake: After Einstein's time travels, when both flames cross Marty and Doc's legs, they cast no shadow, giving the feeling that they are floating, thus giving away the blue screen effect. (00:22:01)
Revealing mistake: When Doc is using a remote control to drive the DeLorean, they show a close-up of the controller. The controller's power meter (the dial with a needle in the middle) shows no power - it's right over to the left. How's he driving with no battery? (00:20:15)
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: When Marty is playing back the Twin Pines Mall demonstration video for Doc, the camcorder tilts itself between shots, judging by the lens which sits higher above the TV set when Doc starts shouting, "1.21 gigawatts." (00:53:00)
Character mistake: At the beginning of the movie Marty is turning on a huge guitar amplifier. The two switches for the filaments are misspelled. They are shown as "filiment." (00:03:25)
Continuity mistake: When Marty tells George how to flirt with Lorraine, they both enter the diner and Marty sits on the back of the counter but disappears between shots, only to reappear later on. Also, the extras around him change, although they're all dressed in similarly colored clothes. Check a man in a plaid jacket next to the blonde girl in pink, who disappears when Marty trips Biff. This continuity havoc was due to the combination of Eric Stoltz scenes and new Michael J. Fox reshoots.
Revealing mistake: Right before Einstein is sent to the future, when a very bright light surrounds the DeLorean, not only is the dog gone, but a black bulky bag has appeared on the passenger's seat. Seemingly a hidden stunt driver or a driving mechanism. (00:21:56)
Continuity mistake: After the DeLorean disappears with the dog inside, flames appear underneath Marty and Doc. In the close-up of their legs, a shot later, the road is spotless and the flames reappear a second later.
Continuity mistake: While Marty is admiring the new truck, Jennifer walks onscreen. Once the angle changes, Marty's left arm is resting on an entirely different part of the door. (01:49:50)
Continuity mistake: When Doc finds Marty's letter in his pocket, the big hook fastened to the DeLorean's passenger side is seen facing the sky. Pretty soon Marty slides across the hood and into the DeLorean, but now at this point it's facing the ground instead. (01:33:35 - 01:35:50)
Continuity mistake: While Marty is at Lou's Cafe, Biff and his gang enter. When Biff starts bullying George, note George's haircut with shaved sides, back (above his neck), and sideburns. In the following shots, George's haircut with its shaved areas change length. This happens again, when George is with Marty and then tries to ask Lorraine to the dance. (00:39:00)
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