Continuity mistake: We discover that because time is non-linear in the Further, it was Josh's spirit who was the one knocking on the door in the original film. However, the knocks we see Josh make in this film don't quite match up with the original film. In this film, he knocks many times frantically, whereas in the first film, we only hear a few faint knocks in rounds of three. (The film tries to mask this by inter-cutting footage from the first film to illustrate the point, but it still doesn't quite match up).
Continuity mistake: When Josh finds Renai on the floor and takes and places her on the couch her head is facing upwards, but in the next shot her head is tilted and facing the camera when Josh smells her, without her head moving.
Continuity mistake: In the first Insidious film, when Lorraine shows adult Josh the photographs, the Lady in Black is seated in the car behind the young him. However, in the second film, when Lorraine shows the photos to young Elise, the Lady in Black seems to be standing in front of the car.
Chosen answer: The third movie was a prequel to the first 2. It was done to set up an explanation in case they made another movie that takes place after part 2, so her appearance after she died made sense.