The type of randomized tear is determined upon entering a room.
The type of randomized tear changes every 2–3 seconds. The item appears to select two tear effects at once, perhaps staggering the times at which each of those effects change.
While not directly a tear effect, 3 Dollar Bill may rotate through Lucky Foot, which may be used to take only positive pills.
If a run is quit, and then continued, 3 Dollar Bill will have a new random tear effect for the current room.
Items that are required to charge like Brimstone or Monstro's Lung can have their charge amount change when gaining a new tear effect, depending on Isaac's new Tears stat. This can cause fully-charged items to need more charge time.
The Proptosis effect is bugged for 3 Dollar Bill, and will only fire half the range it would normally (damage is increased normally).
Unlike Fruit Cake, which can only modify individual tears, 3 Dollar Bill can modify stats as well.