I do enjoy this game; unfortunately, I'm not sure that it is in fact an improvement on the first one. As others have pointed out, the controls are far too stiff for this 4-life system. This stiffness was a problem in the first game too, but it didn't *feel* like a problem there because dying meant restarting one level, not the entire game.
I think that keeping each level as a separate entity is much more befitting of this kind of game. Alternatively, I might suggest an infinite-lives "easy mode" with the current game as "normal" and perhaps even a one-life-only "hard mode". This would be an excellent anti-frustration feature, as it's very irritating to make it to the sixth planet with all 4 lives only to die before reaching the final level (as I did *many* times).
Better response from the controls would also help; there are many jumps that by rights I should've made, but missed because my firm press on the jump button didn't register until it was too late. It becomes very difficult to time jumps when you can't get a reliable feel for when to press the key.
For what it's worth, I think the people complaining about the graphics are missing the point entirely. This isn't a game that needs to look great, and the overall look of the game is both A. an improvement on the original and B. perfectly sufficient to get across the information it needs to.
Overall, it's a perfectly enjoyable little game - great to pass the time, and great for people like me who mainly play flash games for the satisfaction of completing goals. There are definitely some weaknesses though, and unfortunately they're big ones. With some tweaking in that regard, this could easily become a 4 or 5 star game in my book.