Like most damage over time effects, Serpent Sting cannot crit and thus does not benefit from any increases to crit chance. The two piece set bonus from the Windrunner's Pursuit/Battlegear set grants Serpent Sting ticks the ability to critically strike. Each tick then has a chance equal to your ranged crit chance of dealing double damage. The end result is that the damage of Serpent Sting is increased by your crit chance, so that if you have a 60% chance to crit, Serpent Sting will deal 60% more damage on average.
Serpent Sting is a fairly weak damage over time spell, in comparison to those of other classes. To get the most of out it, it should be used in fights that will last longer than 15 seconds. On short fights and trash mobs, the hunter may find it is not an efficient use of focus.
When fighting multiple enemies, it may be useful to apply Serpent Sting to all targets.
Its greatest utility in PvP is against rogues and druids, to prevent them from entering stealth. (Druids can cleanse it, but will have to shift to caster form to do so.)
Be careful using this spell in situations where your group may use crowd control (CC), as the damage will break the effects.
/Patch 3.0.2 (14-Oct-2008): Gained bonus damage equal to 20% of the hunter's Attack Power, up from 10%.
Patch 2.3.0 (13-Nov-2007): Now scales with ranged attack power instead of spell damage. It was considered to be a nature-spell-damage based attack thus was buffed by all nature and general spell-damage buffs including and not limited to: Wizard oil, Improved divine spirit, Wrath of Air Totem. This is no longer the case.
Patch 2.0.3 (09-Jan-2007): "Serpent Sting’s" initial, non-threatening application no longer consumes a charge of Misdirection.