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 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 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)
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)
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.
Visible crew/equipment: When Lucy, Peter, and Susan are riding on the ice chunk down the river, when you see a shot of Lucy struggling to maintain her grip on the ice block, immediately after, there is a shot of Peter holding what was supposed to be Lucy. However, it is not Lucy. The person Peter is holding is bigger than Lucy and had blonde-brown hair.
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: 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 Edmund first enters Narnia, he is attacked by the White Witch's henchman, who pushes him into the snow. In some shots, there is a considerable amount of snow in his ear, and in others, its completely gone. This switches several times. (00:29:15)
Continuity mistake: As Edmund lays prisoner in the White Witch's cell, the long chain dragged along the floor, binding his feet, changes position during shots. (01:03:35)
Continuity mistake: As Lucy, Peter, Susan and the Beavers trek through the snow towards Aslan, their shadows repeatedly change in consecutive shots, such as going from long shadows to their right, to hardly any, to long again.
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)
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.