I've worked on platformers and I know how hard they can be. That said, you hit a lot of the fundamentals nicely, like coyote time and good-feeling movement. I actually thought the downward slash was super rad and could've been the basis of your entire game.
The rough edges are understandable, given the time you had, but aside from the bugs (like jumping after a screen transition), I think I would've just preferred a little more feedback. I didn't really get a good handle on what the enemies were doing or why, why I was getting hit and they weren't sometimes, etc. Also a few issues with the level design, like putting a transition vertically and immediately causing the player to fall into the pit he just came from and take damage.
The art and sound were great, though, and there's a lot of potential with the controls. I'm pleased with this and you should be, too. Nicely done and congratulations!