Continuity mistake: When Lucy first comes out of the wardrobe, it is snowing, and some small amounts of snow are on her hair, but, in other shots, there is either less or more. It keeps switching.
Continuity mistake: When Santa puts his bag of gifts down on the ground, we see that there is a teddy bear and a quiver of arrows, among other gifts, in the bag. In the next shot of Santa reaching into the bag, the bear and the quiver are now next to each other when there were many inches apart in the prior shot. (01:09:30)
Continuity mistake: There are 3 candles on the Beavers' tables during their conversation with Peter, Susan and Lucy. The middle one becomes significantly taller when Susan tells Peter that their mother sent them away from London to escape war. (00:49:45)
Revealing mistake: During the final battle a harness is shown on the water buffalo soldier as the main centaur attacks and kills him (the harness is visible as the soldier is hoisted into the air).
Factual error: The locomotive Bradley Manor has a British Railways number plate on its smokebox door - at least 8 years before Nationalisation. GWR locomotives had their numbers painted on the buffer beam.
Continuity mistake: When being chased by the witch (which turns out to be Santa Claus) across the plain, the shadows change direction between shots, and in the close-ups there is more than one shadow per person.
Continuity mistake: The unicorn that Peter is riding in the big battle scene has a horn, then doesn't, then does.
Answer: Spoiler alert: this gives some important plot twists away. Sometimes a bit of unresolved mystery improves a story, and I think this is the case here. But the book partly answers your questions. At the end of the last chapter it is shown that Mrs MacReady thinks the wardrobe is just a piece of furniture. She knows nothing about Narnia. But Professor Kirke amazes Peter, Edmund, Susan and Lucy by expressing familiarity with Narnia and explaining that a wardrobe might well be a portal into Narnia. If C S Lewis had not written any more books after completing "The Lion The Witch And The Wardrobe" Professor Kirke's knowledge of Narnia would probably have been an unresolved mystery. But C S Lewis later wrote "The Magician's Nephew" which tells how Professor Kirke visited Narnia as a boy. The final chapter of this book says he took an apple back with him, which he planted in his garden. It grew into a tree, was cut down and made into the wardrobe. So Professor Kirke was not consciously aware of what the wardrobe could do, but with hindsight, he realised that he had set up a chain of events that caused the children to discover Narnia.