As soon as the fire is lit, the arsonist's shadow is thrown onto the wall. But as the flames grow larger and spread, the shadow is static, indicating it's a shadow from a studio light and not from the flames.
When Jim Parks goes to check the metal bucket with the burning coals in it, he picks it up by touching the sides of the container. If in fact it was filled with hot coals, the sides would have been very hot and he should have burned his hands on it when he touched it.
When J.R. goes to untie Rita's hands that are behind her back, one can see they weren't actually tied up; she was simply holding them behind her back pretending they were tied together.