I think Assassin's Creed II is an excellent example of sequel improvement. The first game was a lot of fun and had a very intriguing plot, but it could get pretty repetitive. There were a lot of small issues that weren't deal breakers, but were still pretty annoying. One of the most noteworthy being the fact that a top assassin freaks the smurf out when he touches water. Okay, he's got some thick robes and those weapons probably aren't very light, but isn't he overreacting a bit?
Assassin's Creed II had a lot of "oh yeah the old animus had this weird water bug" and "HEY I NOTICED YOU PUT IN SOME SUBTITLES THAT'S PRETTY COOL *wink wink*" Ubisoft fixed pretty much every annoyance and took everything that was neat about Assassin's Creed and made it awesome. The gameplay improved far beyond everybody's expectations while the continuation of the plot was seamless.
Stuff like that is why I love sequels :3