Towards the beginning of the film, Julie takes a picture of young Katie standing in the driveway shortly before a group picture is taken. The photo being taken appears in both Paranormal Activity and Paranormal Activity 2 as an indication that the demon has started haunting them.
As with Paranormal Activity (2007) and Paranormal Activity 2 (2010), Paramount Studios once again utilized paranormal investigator/researcher, Christopher Chacon, who is recognized as one of the world's foremost authorities on paranormal phenomena, to internationally promote and publicize this third installment. Chacon also works in the entertainment industry as a writer, director and producer.
The symbols that appear behind the pictures in Grandma Lois's house are simplified versions of the Pentagram of Solomon (inverted) and the Triangle of Solomon, symbols depicted in the "Lesser Key of Solomon" and used to summon and constrain demons in classical Goethic Theurgy.
The trivia item below may give away important plot points.
In the static at the end of the movie, there is a frame that shows Dennis' and Julie's bed on fire. This is presumably the start of the house fire that is referred to in both Paranormal Activity (2007) and Paranormal Activity 2 (2010).