When Daniel is trying to show Ilonka what a pentagram looks like, he draws a simple hexagon, not a five-pointed star.
What's even worse, they must have used multiple takes, because after a cut, the symbol gets even simpler, and now there is a pentagon on the paper where the hexagon used to be.
When Talbot leaves the ice cave to search for Dr. Frankenstein's records, he has neither socks nor shoes on. But when he enters the next room, where the records are hidden, he's suddenly wearing shoes.
Just after the scene where Dracula dissolves in the sunlight, we see the wagons driven by Doctor Niemann and Daniel pass a sign reading "Frankenstein-1km". If you look past the sign, in the distance you can see a pile of film equipment cases and crates, and even bits of scaffolding used for lighting.
While searching for Dr. Frankenstein's records beneath the ruins of his castle, Dr. Niemann and Daniel discover the Wolfman and the Monster frozen. After thawing out the Wolfman, he then changes back to Lawrence Talbot. Dr. Niemann tells him he can cure him if he obtains the records of Dr. Frankenstein, last observed being read by Dr. Mannering in Frankenstein Meets the Wolf Man during a laboratory scene prior to the castle being destroyed. Talbot immediately proceeds to a another room where he reaches into the wall and miraculously pulls out the record book totally intact and undamaged.
The goof items below may give away important plot points.
When Dr. Niemann removes the stake from the skeleton of Dracula, not only does his body regenerate, but also his clothes. And when Dracula is destroyed by sunlight, his physical form and his clothes disappear, leaving only the skeleton.
When The Monster picks up Daniel in the lab and hurls him out the window, just before he throws him through the glass you can catch a quick glimpse of the guide wire attached to Daniel that helped actor Glenn Strange (The Monster) lift him over his head.