Sprite Facing Responds Late

My game has the main character which has a 2d sprite with animations. However the environment is 3D. You can see it here actually:

http://www.youtube.com/watch?v=jhT_PniyySY

The problem is present in the video also, when you move left and turn right (or otherwise) the animation suddenly changes without any problem. But when you move left and turn up or down, the animation change responds late. I thought it might be because it waits for animation to finish but why it does not happen in the left-right movement then?

My friend suggested me to use animation transition panel on the right because he also suspected that it waits till animation to finish but I don't even have transition between walking and running animations for different directions.

I suspect my facing booleans do not work properly so here how I set it up:

 void Movement()
 {
     anim.SetFloat("horizontalspeed", Input.GetAxis ("Horizontal"));
     anim.SetFloat("verticalspeed", Input.GetAxis ("Vertical"));
     
     if(Input.GetKey(KeyCode.D))
     {
         if(anim.GetBool ("facingRight") != true)
         {
             anim.SetBool ("facingRight", true);
         }
         else
         {
             anim.SetBool ("facingRight", false);
         }
     }
     if(Input.GetKey(KeyCode.A))
     {
         if(anim.GetBool ("facingLeft") != true)
         {
             anim.SetBool ("facingLeft", true);
         }
         else
         {
             anim.SetBool ("facingLeft", false);
         }
     }
     if(Input.GetKey(KeyCode.W))
     {
         if(anim.GetBool ("facingUp") != true)
         {
             anim.SetBool ("facingUp", true);
         }
         else
         {
             anim.SetBool ("facingUp", false);
         }
     }
     if(Input.GetKey(KeyCode.S))
     {
         if(anim.GetBool ("facingDown") != true)
         {
             anim.SetBool ("facingDown", true);
         }
         else
         {
             anim.SetBool ("facingDown", false);
         }
     }
     else
     {
         anim.SetBool ("facingRight", true);
         anim.SetBool ("facingLeft", true);
         anim.SetBool ("facingUp", true);
         anim.SetBool ("facingDown", true);
     }
 }

Please help me with my noobish problem. I would much appreciate.