I've player your demo about 20 minutes.
What I noticed first is that the jump button (gamepad) is "B". I've played a few platformer games a while ago and all of them had the "A" button for jump and "X" or "B" for attack or use. Maybe is just a preference but I would change that <img src="{SMILIES_PATH}/icon_e_smile.gif" alt=":)" title="Smile"> .
When the player hangs on the edge of a platform and I want to jump on it: If the player is facing left and I press the "go to left" button and jump button it won't jump. ( https://www.dropbox.com/s/n7osr87tcqegw ... 6.jpg?dl=0 )
Also, you could eliminate the walking animation while in the air.
Soldiers are very easy to kill in some situations , depending on the position you and they have, and the environment around the player, for example:
If I have some space around me its easy to jump or duck to evade the bullet.
But if I have to jump to evade the bullet and I have a solid object atop (If I am on a long corridor or something) then I can't defend (Maybe a plasma shield for the player would help in those situations).
PS. The game runs smooth at 60 fps on my pc( i5 3300Mhz, 8gb ram, gtx750Ti). The default resolution is 720p ?