You need slightly more time to react to the mines. They go off way to friggin fast imo. Or you could start them off slow in lower levels and make them quicker in higher ones. And give them some kind of visual clue as to how much time they have, like a number that counts down or a meter that ticks off notches or something.
As for the whole falling off the bottom thing, not being able to move forward when you're off the top of the screen is a real pain in the ass. You can get stuck and not be able to advance in the level because the next platform is too far to drop onto. In my opinion, you should do one of two things:
1. Don't allow falling off the bottom. Just make it instant death, and instant restart of the level. Since falling means you'll probably have to restart anyway, automatically doing it for the player will cut down on frustration.
2. Every time you fall off the bottom, you lose a star (or maybe all of your stars?). Counter-balance this by allowing the player to move wherever they want to when falling back into the level. Since the goal is to get as many stars as possible, it's a fair trade off because people wouldn't be able to "cheat" to get past a tough part, but they can still at least finish the level. <-- better option imo
Also, if the player gets rank 3 or 2, have an option on the results screen to "Retry" "Next Level" or "Exit" (to menu). If they get rank 1, obviously it should only say "Next Level" and "Exit." If they blow up from time running out they shouldn't get any ranking results at all, but a fail screen asking to "Retry" or "Exit." And if it were my game, I'd lock levels until you've beaten them once so you can't skip ahead.
Just a couple ideas there