Maybe I'm nitpicking a tad, but...
A "mole," by definition, is someone who stays hidden or blends in; in short, becomes the perfect persona of the group being targeted, though short of actual maliciousness. In other words, Sean Penn may be a mole, but not Michael Moore, if they were conservative moles in the liberal world. Moore causes actual damage against conservatives, while Penn just parrots the cause.
A "troll" is more overt; in fact, he has to be highly noticed. He usually can be discerned because of his "offbeat" or "confrontational" manner. In either case, they are different than a mole.
Obviously, there can be a combination of the two as dynamically required. If a "troll" becomes a bit suspect, he may retreat into "mole" status to avoid a problem; indeed, he may even revert to a position that keeps him in line with the proletariat. Conversely, a "mole's" true worth is not validated until he does something to instigate the masses, so a mole would have to either subvert the membership by collecting information on as many of them as possible, in which case he is actively engaging the enemy, or other means similar to this method.
Anyway, a bit persnickety but nonetheless as accurate as I can make the difference to be.