What are idiomatic or metaphorical expressions with mole the animal?

The use of the term "mole" to indicate a covert agent does not directly represent an idiom, because it suggests stealthy, unobserved activity.

The mole is used in connection with eyesight, e.g. blind as a mole, but not nearly as often as the totally incorrect "blind as a bat."

The most common metaphor has to do with a mole's burrowing. The phrase "making a mountain out of a molehill" means to exaggerate the effect of an activity or event, referring to the very small amount of dirt a mole leaves on the surface.