They are both able to see and interact with ghosts, summon them, and communicate via seance (but the Doyles rarely bother with all that). Mediums can also sense (or be subconciously drawn to) an object with a ghostly aura, such as a murder weapon.
Frank and Sadie are able to generate willpower-based feedback to certain methods of supernatural sway. Sadie has resisted the thrall of vampires and Frank evicted an invading angelic spirit from his body. They both could resist the Pan's influence to some extent, though not completely.
They are, however, fairly powerless against other magical influences, such as the seductive powers of succubi and incubi.
The Doyles have encountered several fraud and/or con artists, who use their knowledge of the supernatural for monetary gain: