Continuity mistake: During the first potion class scene during the movie, Hermione and Lavender are seen standing next to each other while being taught potions by Professor Slughorn. However, within the first minute or so of the lesson, Hermione and Lavender are standing far apart, then in the next shot, they are standing close together, with what looks like barely any space to move. They remain like this for the rest of the scene, but you can see the gap between the two within the first few minutes of the class.
Continuity mistake: The very first shot of Malfoy pulling the tapestry off the Vanishing Cabinet (after tossing a green apple in his hand) is used once again later (after Harry and Luna head off to Slughorn's party), when he is pulling the tapestry off again before placing a green apple in the Vanishing Cabinet. Note the same poof of dust, angle in which tapestry falls, and Draco's body position.
Continuity mistake: When Dumbledore and Harry enter the muggle house to find Slughorn the lights are all out; the only illumination comes from their wands. They enter the hallway, then both turn towards the living room with their wands in front of them. Despite this, the wall behind them is illuminated without either of them casting a shadow. The lighting in the hallway is obviously coming from a different source, not the wands. Can't be moonlight - it is a bright white light shining directly on the wall that was not visible when Harry and Dumbledore first entered the flat.
Continuity mistake: When Ginny snatches 'Advanced Potion Making' from Harry in the common room, and says "Who's the Half-Blood Prince? . That's what it says right here: 'This book is the property of the Half-Blood Prince'", she opens it at a random page in the middle of the book. When Harry sees the words 'This book is the property of the Half-Blood Prince', they are written on the first page. Also, the continuity is wrong as she is shown to switch pages between very quick shots.
Continuity mistake: When Ginny rips the Half-Blood Prince's potion book out of Harry's hand, before Harry gets up from leaning against the couch on the floor, Ginny is nowhere to be found in the chair on the very far left of the screen. As Harry walks around the couch while talking to Hermione, she is suddenly sitting in the same chair.
Continuity mistake: In the scene where Dumbledore and Harry meet Slughorn in the desolated house, some piano hammers lie on the ground. These hammers are from an upright piano but the "restored" instrument later in the scene is a grand piano. (00:06:25)
Continuity mistake: Tied round Dumbledore's beard is a thin silver strand, with dangling silver balls, that changes position and the height of the silver balls differ in consecutive shots, depending on the camera angle throughout the film. For example, when Dumbledore and Harry first pay a visit to Slughorn.
Continuity mistake: At the diner when Harry walks toward the windows, in the close-up of a window through which we see the distant platform (before Dumbledore appears), the style of the window's muntins (sash) around the glass panels is quite different in this close-up, than in the previous shots of the windows. (00:04:00)