Do the leaves of the World Tree (Yggdrasil) have any special properties in Norse Mythology?
I don't know if the leaves had any magical properties, but apparently it dripped honey:
I know an ash-tree stands called Yggdrasill,
a high tree, soaked with shining loam;
from there come the dews which fall in the valley,
ever green, it stands over the well of fate. (Vsp. 19, Larrington)
The dew that falls from it on to the earth, this is what people call honeydew, and from this bees feed. (Snorri/Faulkes, Gylf 17)
(The translations are by Carolyne Larrington and Anthony Faulkes.)
Ash trees exude a sticky sap called manna or honeydew, which runs from the branches and leaves. Apart from bees, the goat Heidrun ate this honey, which probably was transformed into the mead that ran from her udders.