Revealing mistake: When Lucy first meets Mr Tumnus, she looks down at his legs and sees that they are not the legs of a human, but of a fawn. During this shot, Tumnus shifts his legs slightly, and it is evident that the CG legs do not exert any pressure on the snow at all. This mistake occurs at several other points in the film. (00:15:20)
Revealing mistake: When the Beavers and the Penvesies trek along the ice river, the Beavers drag their tails along through the snow, yet the snow is never disturbed by them. (01:03:35)
Revealing mistake: Aslan is carrying Lucy and Susan on his back to the battle and is running at a very fast speed. If you look at the girls' hair though, it isn't moving at all, flat against their backs as if there wasn't any wind. (01:51:20)
Revealing mistake: During the battle scene, the White Witch clearly stabs Peter in the arm with her sword. In the very next shot the sword goes through the chainmail behind his arm, into the ground. (02:02:40)
Revealing mistake: When the girls are on Aslan's back, you can tell that there is a flat screen behind them.
Revealing mistake: When the stone tablet breaks, Lucy and Susan fall down. But if you watch the ground, it never actually moves to make them fall.
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).
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.