It's true the second movie's plot is a little screwy, and the shock of the first movie had worn off by then. But you have to remember a few things to appreciate the sequels.
1. Two (and Three) were done five years after One. They had to reassemble the same cast (all except George McFly, who wanted too much money so he was written out), recreate the sets, and...
2. They had to integrate Two into the storyline of One, recreating many of the original scenes but from different angles. These were not out takes from the original movie -- they actually created them all over again! This had never been done before, revisiting a movie that had wrapped five years before. Nowadays they'd put hooks into the original movies (Star Trek, Indiana Jones) to pay off in the sequels, but at the time of BTTF1, sequels were not commonplace and no hooks had been set. Except possibly for the open-ended ending which fed right into a sequel plot.
3. Age-progression make-up was in its infancy in 1989, and it was pretty crudely done. That was true in the first movie as well.
4. In the scenes where age-progressed actors played in the same shots as their young selves, this was all done with split-screens in-camera. Nowadays they would be composited digitally but in 1989 this was cutting edge stuff. It looks fairly unremarkable now, because since BTTF2 was such a big success everybody started doing it. But before this movie, it was not common.
5. Many of the scenes of 2015, thirty years in the future, they were wildly off. There are no flying cars (Zamekis says he knew there wouldn't be), but he has gas at $6/gal, he has hoverboards, he has weird fashions with computers built into the clothes. He has a future where an ugly extremely rich guy, who builds casinos and motels and puts his name in lights on the sides of them, runs the town. He has electronic newspapers, and handheld tablet computers. The scenes of destroyed Hill Valley, when Marty goes back to a ruined 1985, look remarkably like 2015 New Orleans.
In all, the filmmakers say in the featurette, they got about 50% right -- which isn't bad at all.