What is the Full Preterist perspective on ghosts and paranormal activity? Generally, according to the Full Preterist position, the resurrection of the dead occurred in 70 AD, when all the Old Covenant saints and prophets in Sheol were liberated and allowed into heaven at the time that the Temple was destroyed. This would mean that when people die they either immediately go to heaven or hell upon death.

How exactly are paranormal activity and ghost/apparition sightings compatible with the Full Preterist perspective? Can one believe in ghosts while being a Full Preterist?
Great question and one I have dealt with as I became a full preterist.  

I used to believe in ghosts, departed souls and demons impersonating loved ones through palm readers, etc, but that would mean Biblical verses such as 1 John 3:8 (Jesus came to destroy the works of Satan) would be a hollow statement and actually a lie.  Jesus said the strong man was bound.  (Matt. 12:29). Another hollow victory if Jesus only bound the strongman and not his little demons. 

The word "Destroy" has a different meaning in the context of usage elsewhere in Scripture than to mean just crush.  The only other time Jesus used the word was when He said he could destroy this temple and he would rebuild it in three days.  

The word he used had the meaning of taking all the remaining parts, pounding them into small particles similar to grain, then removing all the particles so that they could never be reassembled.  This was the same "Destroy" that John mentions Jesus did to Satan's kingdom.  

If that was so, then there is no element of Satan's realm left or Jesus and John were wrong or lied.  I choose to believe both were right and we have/are misinterpreting Scripture.  

Summary

If Jesus said he bound the enemy and John Said Jesus destroyed Satan's work, and Jesus said after his resurrection that He possessed all authority and power (none left to share with Lucifer), but he didn't say that before the Resurrection, then it would necessarily cause one to accept that there really is nothing for Satan to reside over.