When Evie helps the maids clean up the broken glass, her sculpture disappears momentarily and her cell phone (that she puts in her right pocket) appears in her left hand.
When Evie and Walt are lying down talking about what they want in life, Walt's head goes from being propped up on his hands at the nape of his neck to being propped up on his hands over his ears in between shots.
When Evie boards the plane to cross the Atlantic, she takes off in an aircraft with 4 engines and an upper deck. When then plane lands in England, it is a different aircraft with two engines and only a single deck.
Earlier in the movie, Maid #4 is seen being attacked in the cellar and having her neck snapped. However, in the scene in Walt's library following Evie's escape attempt, there is another Maid #4 that is seen moving woozily from blood loss. Maid #4 in the library would not be able to move the way she does if she had previously had her neck snapped in the cellar. Snapping someone's neck, in the very least, paralyzes them; at worst, Maid #4 should be dead in the library scene.
In the preface opening, when a character hangs herself. When her head falls from her body, only the head falls implying that the body remained on the piano wire (which wouldn't make sense) or mistakenly forgotten.