1: You can shear Mooshrooms for 2 to 5 mushrooms
2: If you kill them they will drop beef and leather like normal cows
3: You can still milk them with a bucket
4: You can get a bowl of mushroom stew by right-clicking on them with a empty bowl
5: You can breed Mooshrooms with normal cows and the baby will be randomly chosen as a regular cow or a mooshroom
6: It is possible for them to spawn in non-mushroom biomes
7: The Mooshroom is the most resourceful mob (Mushrooms, Milk, Mushroom Stew, Leather, and Beef)
8: If you throw potions of invisibility at a mooshroom, the mooshroom will disappear, but its mushrooms will still be visible
9: They were first added in the 1.9 Pre-Release
10: Mooshrooms are PINK :D

-lazyquackduck