When Oz and Theodora flee from the crash site, Theodora's boots are flat; moments later, when he boosts her into the cave, the boots have high heels.
When Oz is talking to Glinda about leaving and packing his bag, he puts the deck of cards into his bag and the table is mostly empty. Next shot the cards are laying on the table again. Finally, he picks the deck up for a second time and places them in the bag.
When Oz first meets Theordora, his bag disappears from his hands then reappears twice. The first time is when the fairy spits on him and he covers his face, the second is when he conjures the magic flowers.
When Theodora starts to remove her red coat at the camp fire, her pendant disappears between shots.
When Oz and Theodora first meet, Theodora's hat size changes several times between shots and even becomes reversed at one point.
When the lion runs away from the red cloud puff, he produces a growl of a cougar, which is a purring cat (genus Puma). Lions (genus Panthera) are roaring cats. Ozian animals don't share all the details of their Earth counterparts.
When Theodora and Oz are walking in the Sunflower path the orientation of the sunflower heads is towards the path - on both sides. Sunflowers would all face the same direction. Ozian flowers don't have to follow the same rules as Earth flowers.
When Oz is telling Glinda his battle plan, he hands her a book. She thumbs through the book. In the process, you see the exact same page appear twice. It is the one with the trick box diagram. The wording on the pages is exactly the same.
The basket of the balloon is about waist high to Oz. It falls into the water and sinks completely. However, when Oz stands up the water only reaches his mid-thigh showing it is much too shallow for the basket to completely sink.
The balloon is not a hot air balloon, but a hydrogen balloon. Such balloons were the only practical balloons of this period, before compact propane fuels were available. They are recognisable by being smaller and spherical, without the lower opening of a hot air balloon. And of course, they don't need a burner.
Oscar says his grandmother was "a decorated war hero". A man of 1905, when gender differences were strictly observed, would have used the word "heroine".