Dispensers can fire snowballs but they don't hit mobs (hostile and passive).
It is the same problem with eggs, but all is good with arrows.
Code analysis by @unknown in this comment
Linked issues
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Yes, MC-44280 says that snowballs don't knockback mobs, while this report says that they don't even hit the mobs. This isn't a duplicate.

Is this still the case in 1.9?
confirmed for 1.9
further testing showed, that mobs aren't affected, that stand right in front of the dispenser, while those that are a few blocks away get hit. http://imgur.com/istJ6w6

Please change the title to "Throwable items fired from dispenser do not hit mobs for the first two ticks"
And please update the description, the word "irritate" does not fit very well

Please link to this comment in the description
The following is based on decompiled version of Minecraft 1.9 using MCP 9.24 beta. All method and class names are the names used in the decompiled version.
The reason why this happens is because the net.minecraft.entity.projectile.EntityThrowable.onUpdate()
method only tests if the thrown entity hits a mob if it existed for more than two ticks. This delay should be only applied if the thrower is an entity.
/**
* Called to update the entity's position/logic.
*/
public void onUpdate()
{
//...
Entity entity = null;
List<Entity> list = this.worldObj.getEntitiesWithinAABBExcludingEntity(this, this.getEntityBoundingBox().addCoord(this.motionX, this.motionY, this.motionZ).func_186662_g(1.0D));
double d0 = 0.0D;
boolean flag = false;
for (int i = 0; i < list.size(); ++i)
{
Entity entity1 = (Entity)list.get(i);
if (entity1.canBeCollidedWith())
{
if (entity1 == this.field_184539_c)
{
flag = true;
}
// Replaced this
//else if (this.ticksExisted < 2 && this.field_184539_c == null)
else if (this.thrower != null && this.ticksExisted < 2 && this.field_184539_c == null)
{
this.field_184539_c = entity1;
flag = true;
}
else
{
//...
}
}
}
//...
}
Fixed as suggested by Marcono1234
this is a seperate issue. snowballs don't affect mobs at all, they fly through mobs