It's already looking pretty polished!
The user interface designer in me says you should skip the "next" button on the tutorial and just make it so clicking anywhere goes next, too. Same for the "play" button in the tutorial.
It starts off like a snail... I would say it should start off as if you were 30 seconds or so into the game. The difficulty ramps up pretty quickly, but I think it's at a good pace.
Whenever you get a combo, it'd be nice if it gave you more of a visual award. Right now it's hard to tell that you're even getting more points. How about making the text larger when the points are of a higher value? That way when you get really big combos, you really know it.
I would've liked a few more sounds for the firing. That "pew" got a little old pretty quick.
It's pretty hard to see when you're on the green screen. It also seemed like a weird transition since the previous transition just added that galaxy.
The red stars on the pink background are
super hard to see. If it weren't for their tails, I wouldn't have noticed them at all...
K, now I've died... at least I got 49060 as my score.
Fortunately, I can say I did not find a single bug! That almost never happens!

This is really great, and I imagine it will translate well to a touchscreen device. I agree that you should probably add more enemy types, as there wasn't a lot of variation besides speed and number. I don't think I would want the bomb button if it were only one use, plus it would add a bit of clutter to your interface, which is ultra-minimal (a great thing!).