I like that there is basic controller support, even though it's not stated. That being said, if you die, there is no way to press the respawn button with controller, and the Y button feels unintuitive for a jump.
As for the regular controls, they feel pretty good, but my thumb automatically goes to space bar for jump, so it might be an idea to have multiple buttons that do the same thing. Also, I would do away with the mouse completely (I find locking the cursor coordinates to a corner of the screen works great). I would make the escape and back space button bring up a dialog box asking to quit game or restart level. And I would make the Enter key work to respawn the player.
I like your slow fall mechanic, but I would make the button for it on the other side of keyboard, because it feels a bit awkward on the left hand.
Good job and good luck :)