Corrected entry: Einstein, Dr. Emmett's dog is the first to travel in the time machine. He travels one minute into the future during which he ceased to exist in the current time only to reappear one minute later. According to this it hence would be impossible for the Doc, Marty and his girlfriend, Jennifer, to travel into the future and see their futures as they would have ceased to exist as of when they left the current time until they reappear in the time they set hence impossible to have continued their normal course of life and exist in the future.
Corrected entry: Between scenes Marty's shoes change, e.g. in the skateboard chase scene he is wearing black converse shoes, but when he is in the time machine travelling back to 1985 he is wearing white Nike trainers.
Correction: Not a mistake. After Marty says "Yeah, I can spend a week in 1955." Doc says "first, we have to get you out of those clothes" - this is so Marty blended in with current fashions of the 50's. When Marty is going back to 1985, he claims that he isn't going back in his 50's clothes - "you think I'm going back in those clothes?.", or something to that effect. It was all done to make Marty less suspicious to the people around him.
Corrected entry: Right when Marty returns to 1985, and has to run back to the mall, we see him call the drunken bum on the bench "Red". In 1955, "Red" is the first name of the mayor running for re-election in one of the first shots of the town we see. (01:38:20)
Correction: While their names are similar, Bob Gale confirmed on the DVD commentary that Michael J Fox improvised the name on the day and "Red" isn't mayor elect Red Thomas from 1955. It's also a different actor playing the bum vs. on the poster.
Correction: The series makes it clear that the timeline is highly resistant to changes, and that when you make a change to the timeline, there's a delay before those changes impact the timeline. This is why Marty saw the photo of him and his siblings slowly fading rather than instantly disappearing as soon as he interrupted his parents' getting together. In the second movie, Jennifer and Marty weren't in the future for long enough to start impacting the timeline.