This item usually charges much faster by moving than attacking.
Considering a movement speed of ~400 units per second (with normal T2 boots), moving gains 20 charges per second, while an average attack speed with just the Shiv and level a normal level 18 champion of ~1.2 attacks per second grants ~12 charges per second (given the average possible attacks to generate charges) moving is roughly 60% faster.
The lightning effect's damage is affected by all damage modifiers and critical damage modifiers like Infinity Edge and DeceiveShaco as well as runes and masteries.
Runaan's Hurricane charges Statikk Shiv's passive up to 3 times as fast by autoattacking with enough targets in range of Runaan's effect, which means charging by autoattacking is technically an on-hit effect. This allows you to gain 30 charges per autoattack, and synergizes well with the attack speed bonus on both items, as this combination also gives 110% attack speed, further improving its passive.
The visual effect for the lightning arc originates from the initially attacked target rather than from Statikk Shiv's user.
The passive magic damage will only critically strike if the associated attack critically strikes.
Statikk Shiv passive's damage does not proc spell vamp.
When activating both Electrical SurgeKennen and Statikk Shiv's passive within a small enough window, whichever was casted second will not have the sound effects replay (due to the previous exact copy of the sound just previously playing).