Corrected entry: When doc picks out clothes for Marty to wear to the old west, Marty asks if they are authentic, so Doc says "sure, haven't you ever seen a western?" Considering Doc is supposedly a genius and the old west is his favorite historical era (he himself said it was his favorite era in part 2) he should know that Hollywood's version of old west clothing and the reality of it are two different things. Doc should know better than to base his knowledge on Hollywood films.
Corrected entry: When Seamus McFly goes to comfort his crying baby son William, we can see that he is a very affectionate father. This was practically unheard of in the 19th century. Children were routinely beaten for even the smallest infractions at the time, it was the norm. Since William was only an infant, I doubt he would be beaten, but his father would not be so kind towards him either. His attitude would be more like "shut up kid, what are you crying about now?". The whole concept of being affectionate towards one's children is more of a 20th century idea.
Corrected entry: When Doc and Marty locate the time machine in the mine/cave in 1955, the door/entrance to the mine cave is too small to have been used in 1885 to get the time machine into the mine cave. Others have said that Doc had the intelligence and time to disassemble the car/time machine, carry the parts in and re-assemble it inside the mine/cave. The problem with this is that while many parts (engine, doors etc.) could be disassembled, the body and frame can only be disassembled so much, they would still be too large to get through the door. Doc would have had to cut them up, carry them in, and then weld them back together. There were no signs of a welding process (weld bead) on the roof, which is part of the one-piece body. Since the body is stainless steel, the welds could not be sanded down and painted over, and there is no paint.
Corrected entry: In the letter the Doc sends to Marty in 1955 telling him where to find the time machine and telling him not to come back to 1885 to rescue him, he says he has met a wonderful woman and is thinking of settling down with her. When Marty goes back to 1885 the day after the letter was sent, the Doc has not met Clara yet and does not appear to have any other female attachments.
Corrected entry: When Doc and Marty are in the blacksmith shop, Doc reads the picture tombstone: Shot in the BACK for a matter of $80. Even Buford emphasises this in the previous scene; "one day you gonna get a bullet in your back". However, in the festival scene when Buford is about to shoot Doc, Doc is facing FORWARD. If Marty had not been there to stop the bullet with the frisbee, Doc would have been shot in the chest, not the back. (00:36:00 - 00:58:45)
Corrected entry: It would have been a lot easier for Doc to construct a rudimentary rocket using gunpowder as the propellant than the highly unlikely solution that he ended up doing. He could have attached two pipes, either side of the car. Gunpowder from bullets, shotgun cartridges etc. Wouldn't even need the railroad wheel conversion although I reckon would be better on rails than a dirt road.
Corrected entry: Why would Doc label the toy car "time machine" when they both knew what it was? Having the car marked like that would only make sense for Clara to see it when she arrives at the livery so she would assume that Doc was telling the truth when he told her he was from the future. Since Marty and Doc wanted to minimize their true identities and their association with the future, they should have covered the train set up, just in case they failed in their attempt and/or had to come back.
Corrected entry: Once Bueford went to jail, there was no hurry to get back to the future; as they did not have to leave before one of them got shot. Bearing that in mind, why did they chase after the 8 o'clock train? They didn't have much time to do that, which made it extremely difficult. They could've easily just used a train on a later date, one with plenty of time to plan out the experiment.
Corrected entry: In the scene where Doc explains to Marty the idea of pushing the DeLorean across the bridge, Marty points out that the bridge is not completed yet (in 1885). Doc says that Marty is just not thinking 4th dimensionally, and once they return to 1985, the bridge is complete, safe and still in use. Unfortunately, the whole idea of returning to the exact same point in space, but a different time, is fundamentally flawed. If the DeLorean was to return to the same point in SPACE, only 100 years later, it would have to account not only for the completion of the bridge, but to all of the other changes to the physical environment. For example, in 100 years, the North American continent would have moved because of continental drift, the Earth would have rotated on its axis, so that point in space would no longer be Hill Vally, CA; the whole planet is revolving around the sun, therefore, the planet Earth wouldn't be in that exact point in SPACE, the sun is revolving around the galaxy, the galaxy moves through the universe, and on and on. Anyway, the DeLorean couldn't have shown up on the completed bridge 100 years later because Earth is moving through space in several different ways.