Bad picture quality
The color timing was bad, and if you adjusted the brightness so that the indoor scenes were right, the outdoor scenes (the wedding especially) looked too bright / overexposed. And if you reduced the brightness to make the outdoor scenes look halfway decent, the indoor scenes were too dark / full of crushed blacks. There were a few scenes that looked good (but not great), as well as one scene that looked especially bad (that particular scene looked like it was shot on 16mm).
I don't know if the problem was with lazy/incompetent filming or if it was the result of a lazy/incompetent digital mastering and/or transfer to Blu-ray.
I find it strange that the biggest, mega classic movies often end up looking like crap on Blu-ray, while relatively small-time movies like Quigley Down Under (1990) and A Nightmare on Elm Street (1984) look spectacular. One notable exception is Spider-Man (2002), which was a huge movie, and was one of the best looking movies I've ever seen. It looks way better than any of the Marvel Cinematic Universe movies (which started in 2008), especially the most recent ones that were shot on video.
In any case, picture quality aside, I'm glad I watched the movie. I thought for sure that I'd already seen it ages ago, and that I didn't like it. I clearly remember renting it in the early 1990s when I was 16 or 17; it came on two VHS tapes, held together with a rubber band. But it must have been part II or III that I rented, because nothing about this movie looked familiar as I watched it tonight, and I thought it was quite good. It isn't the best movie I've ever seen, but definitely the best mob movie I've ever seen (a damn sight better than Goodfellas, which I think is overrated).
There were a could of things I didn't like about it though:
1. I couldn't always understand what Marlon Brando was saying, and had to rewind and turn on the subtitles several times.
2. There were some Italian language scenes for which there were no subtitles (the subtitles just said, "Speaking Italian"), most notably the scene where the guy is speaking in Italian to Michael Corleone in the restaurant. Some Italian language scenes had subtitles and others didn't; there should have been subtitles for all of them.