I'm pretty much copying the content of my review of volume one of this set in that I praise that one and pretty much have a so-so assessment of this one.
TCM Greatest Classic Film Collection: Astaire & Rogers (The Gay Divorcee / Top Hat / Swing Time / Shall We Dance) is essential for someone who doesn't really know this dancing duo that well. This volume is really for the completist. "Flying Down to Rio" and "Roberta" don't even star the pair. Gene Raymond and Delores del Rio star in the 1933 precode "Flying Down to Rio" and Ginger and Fred are fourth and fifth billed feuding - and dancing - members of an American troupe that is performing in Rio. Its main virtue is that it is a precode and therefore some of the lines and situations are priceless. "Roberta" stars RKO's queen of the lot at the time - Irene Dunne - and Randolph Scott before he found his niche in westerns. It's a good romantic comedy, but just don't expect too much of Fred and Ginger. "The Story of Vernon and Irene Castle" is the last film the duo did together for RKO and is ironic because, if the Castles are remembered at all today, it is because Fred Astaire and Ginger Rogers played them in a movie. Plus, because the two are happily married in the film, you're missing all of the fun of the misunderstandings, squabbling, and sexual tension of their other RKO starring vehicles. "Follow the Fleet" stands alone in this set as one of the best that Astaire and Rogers did together. There's lots of great music and a good supporting cast. It's just too bad that in this second volume that there wasn't room for "Carefree", since it is one of the few films in which the plot has Ginger putting one over on Fred rather than vice versa.
If you are really that big of an Astaire/Rogers completist maybe you should consider Astaire & Rogers Ultimate Collector's Edition (Flying Down to Rio / The Gay Divorcee / Roberta / Top Hat / Follow the Fleet / Swing Time / Shall We Dance / Carefree / The Story of Vernon and Irene Castle / The Barkleys of Broadway). It's been around long enough that it is usually always on sale somewhere and it is much more durably packaged than these Greatest Films Collections tend to be.