Although Scott Carey grows increasingly smaller, the pitch of his voice never changes. The pitch of a person's voice is primarily dictated by the size of the vocal chords; as he decreases in size, his voice should have increased in pitch, eventually becoming inaudible to human ears.
Shrinking from 6 feet to 6 inches means a scale reduction 1:12 which means that volume, and then weight, reduces in a scale 1:12 cubed. If a 6 feet man weights 80kg the shrunk version would weight 46 grams. He should have moved much faster. In the cellar he is about 3 inches and he weights about 2 grams. He should have climbed with no efforts.
When Scott is crossing the hole in the crate by holding onto a rope and walking on the ledge of the paint can, the extra rope that should be hanging in the hole stays horizontal, revealing that the hole is, in fact, not a hole. It is especially visible when he gets to the other side and pulls back the rope towards him.
Look carefully when Scott is running from the cat and from the spider. In the close-up shots Scott has a shadow. In the distant shots he has no shadow because he wasn't really there, he was just placed on top of the film!