Would you buy a home with a mole in the backyard?

Moles don't harm anything other than your gr - they're just looking for food (afterall the house was built on THEIR land...not the other way around). You can have an exterminator out to trap them as part of your offer if that's what you want...and btw there's no such thing as "a" mole - where there's one, there's a family of them.