A neat little game!
There were some times I got the feeling something odd was going on, like an unsuspected explosion but never to a point where I could trace it as an actual bug.

I dont think I saw all powerups come by and some seem to appear more often than others (like the (annoying) instant death powerup (down?)). But I suppose its easier to evade those more easily if you only have to control your own character, instead of both (I didn't have someone near by to play together).

K42 already mentioned most things, like control handling. (Perhaps joystick control?/ custom control settings?) I also agree with the rope detection, it could be increased a bit. A score counter would make a nice addition.

Other than this its great, I'd say spice up the graphics a bit and you have a great remake!