Noticed that arrows do not despawn from farmland. First noticed when firing at a mob in a field and found the arrows still there several game days later.

Easily reproduced at a different location as a test.

Fired several arrows, first at the farmland tiles, then at normal (grassy) dirt squares nearby. The arrows on the farmland remained while the dirt arrows disappeared.

[Added]

Arrows can only be picked up off of farmland after digging up the block first. You will then hear the impact sound and the arrow will be sticking out of the ground to be retrieved.

Do not know if mob arrows behave the same