So if you watch about 35 minute of this movie, marty point at a telephone book in close up but it is horrible hand, you can see small wrinkle and crease and dirty old nail
But then in next shot you can see he has young fresh skin hand
So what is this old hand purpose? I think it is to do with time travel
Similarly, did you ever see 'Scrooged'? There's a scene where Karen Allen's character gives Bill Murray's Frank Cross a business card. We see a tight close-up scene of a hand passing off a business card to another hand in a very methodical way.
It's such an unnecessary scene. Who hasn't seen someone hand a business card to someone?
I've seen it numerous times. There's nothing unusual about the card, or the hands AFAIK. Why make such a special show of it?
Well, it's either Eric Stoltz - as wearsalan pointed out - or a double for the close-up shot. It's probably 1000% more expensive to get Michael J. Fox in to record a hand closeup than to have a double stand in for him. Especially since he was shooting Family Ties at the same time as Back to the Future, Zemeckis and Co. were probably maximizing their use of the lead actor.
It's called an insert, and they do it all the time in movies and TV shows. The inserts are typically shot at a different time and in a different location than the main scenes (usually by a second-unit team), and they don't generally use the stars because they seem to think that hands are more or less interchangeable, as long as they belong to someone of the same sex and age range, and they aren't too fussy about age range. Generally it's just three age ranges: child, young-to-middle-aged adult, and elderly:
They messed that up in Titanic. It was James Cameron's hands drawing Rose and it was pretty obvious not Jack's. Of course it helps that 98% of the male population wasn't looking at his hands .
I know in The Wrath of Khan they filmed all the close up scenes with people interacting with the controls on the bridge and the displays after they finished with principal photography with the main cast.