Play as Doc — While the movies and the series tend to focus more on Marty then anything, I've always found myself more relatable to Doc and I was disappointed that this was never an option. While not as the main game, it would be nice to have a few scenes where you're Doc (possibly helping Marty or the like).
Interaction with the Browns — Going back to my favoritism to Doc, I was also disappointed to have not seen Clara, Jules, or Vern in the series (only being mentioned in name only). It would've been nice to see and interact with them in some fashion.
Back to 2015 — Just as the envisioning of 2015 was meant to be a joke (my favorite being the public fax machines attacked to mail boxes), I still think it would be fun to revisit this year or any "future" date for the BTTF timeline. I would want this future to remain as is (flying cars, hover boards, TV glasses, etc.), but possibly with some jokes relating to them compared to OTL. Maybe something like "Lehman Brothers opens branch in the Soviet Union" or something to that nature. Something to the tune of 1955 Doc's "made in Japan" joke.
Focus on different periods — We've seen the 1980s, 1950s, 2010s, and the 1880s within the trilogy, while the 1930s were explored in the games. I would favor choosing another period in a second season.
Homage to the original script for BTTF II? — This idea I thought of when I came across the original script for BTTF II. It was mostly changed when Crispin Glover (George McFly) refused to take part in the sequels. Instead of going back to 1955, Doc and Marty were to retrieve the almanac from Biff in the 1960s. Reading the script, a couple of interesting jokes came up and I've always wondered what might've been. It might be interesting to see these jokes be used here.
Eric Stoltz — I remember reading years ago (before DVDs and the Internet) that Eric Stoltz was originally cast to play Marty but was cut after five weeks of shooting. I recently thought of a concept in which a Stoltz-like character is introduced and potentially could be an "Anti-Marty." My idea is that the timeline when Marty meets Doc is screwed up, in which Doc instead befriends "Stoltz." Marty tries to change this back, only to be fought by "Stoltz" (who doesn't want to loose his friendship and adventures with Doc). Definitely an earth-shattering adventure. Also add John Lithgow to the mix (who was the second choice for Doc had Christopher Lloyd refused the role).