Continuity mistake: When Edmund speaks with the White Witch the first time, as he eats the Turkish Delight candy, the amount and pattern of powdered sugar that remains on his lips differs in the following shots, depending on camera angle. (00:31:10)
Continuity mistake: When Peter finds the note about the capture of Mr. Tumnus he pulls it down off the nail, ripping the top edge of the paper. In a following shot the top edge of the paper can be seen fully intact, then ripped again. (00:41:20)
Continuity mistake: After falling through the wardrobe the first time, when Lucy places her hands on the snow covered lamppost, she leaves marks on it which repeatedly change in the following shots. (00:13:50)
Continuity mistake: When Lucy is at the lamppost the first time, in one shot she has her right hand on the post, in the next overhead shot, her left hand is on the post. The next shot, her right hand is back on the post. There is no time for her to switch hands. (00:13:35)
Continuity mistake: When Mr. Tumnus meets Lucy, the amount of snow on his umbrella differs. (00:14:40)
Continuity mistake: When the four children are waiting for Mrs. Macready to pick them up, a car drives by leaving tire tracks in the dirt road. When the horse drawn cart comes up the road towards them, the car tracks have vanished. (00:07:10)
Continuity mistake: When Susan shoots the arrow into the target, in following shots the arrow's position differs. (01:27:25)
Continuity mistake: When the train is pulling away from the station, the Penvesie children are leaning out a door window waving, and the small compartment window next to them is open, with hands sticking out, waving goodbye. In the following shot no hands are sticking out the window. (00:05:00)
Continuity mistake: When Edmund is eating the turkish delight, the shape/size of the pieces he eats differ, due to the bites changing between shots. (00:31:10)
Continuity mistake: When Lucy and Mr. Tumnus first meet, he drops his packages on the snow covered ground. The positions of the parcels are quite different in the overhead shot, as Lucy walks over to Mr. Tumnus. (00:14:00)
Continuity mistake: When Edmund is talking to Peter after they've found out that Aslan has died, Edmund has a cut on his lip for most of his close-up shots. But after Edmund says, "Aslan believed you could and so do I," in his next close-up shot, the cut on his lip has disappeared, but it reappears later.
Continuity mistake: When Edmund first enters Narnia, he falls backwards out of the last of the coats and onto the snow. There is a close-up shot of Edmund as he lands on his back, and we can see a sprinkling of snow already on the front of his robe. In the next shot, he sits up, and the front of his robe is immaculate. (00:27:20)
Continuity mistake: When the Pevensies are playing hide-and-seek, there's a shot of Lucy running up the stairs. If you look closely, she is wearing the dress that she wears in her third time to Narnia, not the dress that she was wearing when she goes through the wardrobe into Narnia for the first time. (00:10:55)
Continuity mistake: After Lucy pulls the cloth down, off from the wardrobe, its position on the floor drastically changes in following shots. (00:11:35)
Continuity mistake: In the White Witch's castle, when Edmund speaks with her about Aslan, his shirt collar goes from being over his sweater, to under, then over again.
Continuity mistake: After Lucy and Mr. Tumnus meet, when they pick up the scattered parcels their positions in his arms differ, and the string/bows tied round them differ repeatedly between shots.
Continuity mistake: As Jadis, the White Witch, and her army approach, and subsequently battle the army of Aslan, both army's collective shadows differ throughout this scene.
Continuity mistake: As Lucy watches the dazzling display in the fireplace, she alternately holds her cup down on the saucer/up by her face. (00:20:10)
Continuity mistake: When Peter, Susan, Lucy and the Beavers arrive to Aslan's camp and see Oreius, his body is all black. In the battle you can see that Oreius has black legs up to his knees, but then his body is brown. It's easy to see just when the Minotaur drops from Oreius's back: the stomach is brown.
Continuity mistake: When the Pevensie children leave Mr. Tumnus' home they hear noises outside, so Susan places her hand on Peter's arm and Peter holds her hand. Just before Beaver appears, in the front shot, Susan and Peter remove their hands, but in the next shot they're back on Peter's arm. (00:44:50)
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.