Relating to the sling:
-The mass distribution of the sling
-The shape of the sling (which determines air resistance)
-Elasticity of the sling
-The pouch which may impart spin or give a more or less clean release

Relating to the projectile:
-Mass of the projectile
-Density of projectile
-Shape of projectile which determines aerodynamic effects and interaction with pouch
-The impact effects on various targets (due to above factors)

Relating to the slinger:
-The forces applied to the end of the sling throughout the throwing motion
-The point of release (and cleanness(?) of release)

I think that captures most of it...