Factual error: During the opening WW2 battle scene, the German pilot's boots have modern Vibram soles. (00:01:00)
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 the four Pevensie children are standing on the Coombe Halt platform, waiting, Susan is holding her brown suitcase in one shot, then in the next shot it's on the floor, and she picks it up once again. (00:06:50)
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)
Visible crew/equipment: When Mrs. MacReady meets the Pevensie children at the train station, the reflector screen is reflected in the lenses of her glasses, as she looks down when she speaks to them. It is also visible when the children first arrive at the house, when Mrs. MacReady says, "There shall be no disturbing of the professor." (00:07:30)
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: When Lucy pulls the cloth off the wardrobe, a corner of it lands on her head with heavier side on her right so that for it to completely fall, it would have to fall either behind or or on her right. However, when the shot changes, it shows the cloth falling in front of her, not even coming in contact. (00:11:55)
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: 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 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 Mr. Tumnus meets Lucy, the amount of snow on his umbrella differs. (00:14:40)
Continuity mistake: After Lucy gives Mr. Tumnus one of his packages he dropped, he puts it under his arm. The package is rectangular, yet in the next shot we see a long tube shaped package is under his arm as well. (00:14:50)
Continuity mistake: When Lucy first enters Narnia and meets Mr. Tumnus, she hides behind the lamp. When she comes out from behind it she has snow up the front of her dress to her waist. In the next shot she only has snow at the hem of her dress. (00:14:50)
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)
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 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: After Edmund falls through the wardrobe, into Narnia, his hair changes from bushy, brushed back and messy, to suddenly flat and combed between shots. (00:27:25)
Continuity mistake: When Edmund falls backward into the snow, after his near hit by the White Witch's sleigh, his dressing gown changes from hanging down over his knees, to folded back, over his chest. (00:28:45)
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)
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.