(at around 42 mins) Exterior shots of the abandoned hospital clearly show it has 5 floors. Later when in a flashback Lorraine enters the lift with Parker already present. Lorraine presses the button for the ground floor. The camera then clearly shows the lift services 10 floors, despite the hospital only having 5.
(at around 1h 18 mins) While in The Further, Josh approaches his old house and begins to knock on the door. You can see there is no screen door attached. However, in the first movie, and in the "flashbacks", there is one.
(at around 3 mins) There is a photo of Josh as a child standing in front of a car holding a dog that reveals that a spirit is watching him. In the first film, the spirit appears as a reflection in the windshield. In the second film, the same photo shows the spirit standing in the background behind the car instead of appearing in the windshield.
(at around 28 mins) When Lorraine is startled by the baby walker in the piano room, the grandfather clock changes time between shots.
(at around 1h 7 mins) When Carl, Specs and Tucker are in the van preparing to confront Josh, the liquid in the tranquilizer syringe is green. When Carl next pulls the syringe from his pocket to use it on Josh (at around 1h 11 mins), the liquid is clear.
(at around 1h 25 mins) As Josh Lambert throws a kettle at the back of Renai's head, the wig falls off the stuntman playing Renai.
When Renai runs into the cellar and pulls the switch to turn on the light, the room is illuminated, but there is no bulb.
(at around 1h 16 mins) The dashboard shows that the back doors of the VW are open, presumably to allow the crew to film from the rear seats.
(at around 1 min) In one of the scenes that take place in 1986, the car is a from about a decade after that.
(at around 23 mins) When Specs and Tucker walk down into Elise's reading room, the camera crew and a red light from the camera are reflected in a hanging on the wall.
(at around 1h 19 mins) Camera shadow cast on the door, prior to Josh and Carl setting off the security alarm at the old Lambert residence.
(at around 1h 30 mins) When the family runs down into the basement and the son says that he's going to "find his father", someone runs out of the view of the camera.