When Maleva, the Gypsy woman, asks to see Larry Talbot's wound from the wolf bite, he unbuttons and spreads his shirt front (with his bared chest outside the camera's view). Talbot then proceeds directly home where he begins to change clothes. He removes his shirt to reveal that he is wearing a T-shirt underneath.
Bela the Gypsy transforms into an actual wolf, not a wolf/man. When his body is discovered, his feet are bare but he is wearing a shirt and trousers. The wolf killed by Larry Talbot was not wearing any clothing.
When Maleva first puts the charm around Larry's neck, it is dangling on the left side of his tie. (over his heart, like she said.) When he pulls open his shirt to show her his wound, the charm has moved to the right side of his tie without him touching it.
When Larry looks through the telescope at the beginning of the movie, the image is shown is right-side up. Astronomical telescopes turn the image upside-down. While they can be fitted with a special prism to turn the image right-side up, they usually are not since usually there is no practical reason to do so.
When Larry starts to transform for the first time, he has removed his medium-shade suit jacket, tie, shirt, shoes and socks, leaving him in an undershirt and the suit's trousers. Somehow, after his transformation into the Wolf Man he is wearing a dark, long-sleeve shirt and matching trousers. However, when he regains his normal form with no memory of what has happened, Larry notices his different clothes, although this mysterious change is almost immediately forgotten and never explained.
After Larry Talbot has been bitten, we see the Talbot family butler open the living room door to let Larry stumble in, all in long shot. Then it cuts to a close up that repeats the action exactly, including the butler reopening the door.
When Larry Talbot sits on the chair of his room and first changes into the Wolf Man, you see only his feet change. However, when the Wolf Man stands up, the pant legs ride up from his furry Wolf Man feet and you can see bare skin on his legs above the top of the "Wolf Man feet" boots he is wearing.
The goof items below may give away important plot points.
All of the animals react to werewolves throughout the movie, such as a horse that gets frightened when Bela becomes a werewolf and when Frank Andrews's dog barks at Larry Talbot after he's bitten by the werewolf. However, when two of the hunters walk into the woods with dogs to help them track the wolf, Larry Talbot walks up to the hunters and their dogs do not bark or react to Larry at all.
The Police find Lawrence's cane next to the body of Bela and initially classify it as the murder weapon, but they decide that the killing was an accident so it would make sense that Lawrence would be able to use it again within a day.