The amount of spaghetti on Alex' plate increases after he has already eaten some of it.
Just before Alex and Miss Weathers fight in the health farm, the room is full of cats. During the fight, the panning camera reveals that there are no cats in the room. The cats mysteriously reappear immediately after the battle.
The first time Frank pours the wine, he pours it to the same level in the glass twice. Then, the amount in the glass decreases without Alex drinking any.
In the marina scene, George is seen wearing his hat as he gets up in the shot of Dim falling into the water. Moments later as Alex is cutting Dim's hand, George is doubled over in the background without his hat. As Dim falls backward in recoil from the cut, George is seen in the same position with his hat on.
When Alex returns home to discover that his parents have taken in a boarder, he becomes ill and falls against a bar in the living room. As he does so, the liquor bottles on top of the bar are jostled. Some are moved and some fall down. The bottles appear in different positions in the next scene.
The writer's typewriter appears to have perhaps ten or more sheets of paper loaded on the roller. Even if you were making carbon copies, the limit would be three sheets of paper, and two thin sheets of carbon paper. There are no signs of any carbon paper being used at this desk however.
Many of the continuity errors are not in fact errors. Stanley Kubrick purposely included many continuity errors as a way of creating a feeling of disorientation for the audience. That is why people's positions change, props are reorganized, and hats (and other articles of clothing) appear and disappear.
At 19m 45s Alex's mom is supposed to be shouting at him outside his bedroom door. She appears to shouting at the inside of a front door (two locks and a handle), but it is later revealed that Alex has installed extra locks on his bedroom door (including a combination dial lock).
The wine Alex drinks appears far too light in color to be a 10 year old Medoc. Stanley Kubrick did use the actual wine described by Alex (specifically a 1960 Château Saint-Estèphe Médoc). But after each take water was added, ostensibly to keep the wine level consistent without intoxicating Malcolm McDowell. By the time Kubrick got what he wanted the wine was visibly watered down.
All of the newspaper reports seen are merely photographs, headlines or opening paragraphs placed over the original text. One report on Alex, for instance, goes on the reference "the Frothblowers Association and the Striptease Lovers' Association".
At the beginning of the movie, it's cold enough to see the breath of Alex and the droogs, but when the tramp is speaking, we don't see his breath.
When the brutal police try to drown Alex in the water trough, you can tell that the water has been warmed because there is steam coming from it.
When riding in the sports car at very high speed, Georgie is not holding his hat, so it should fly off.
When the rampaging Alex is performing "Singing In The Rain," leaning over Frank, his mouth is not moving.
When the two policemen try to drown Alex in the water trough, we can still hear his voice unimpeded.
In the music store, the camera is briefly reflected in the mirrors to the right.
When Alex and the Cat Lady are fighting at the house, the shadow of the camera can be seen on each of them.
Alex's last name is inconsistent (see trivia). When he goes into jail, he gives his name as DeLarge, but the newspaper articles call him Burgess.
There is a running theme of the Government referring to Citizens and the State, implying that Great Britain has abolished the monarchy in this "future". Yet the prison is called "HM Prison Parkmoor", HM being a common designation for Her/His Majesty.
Alex comments that the opera singer's voice makes "all the malankey little hairs" on his skin stand up. In the Nadsat slang that he speaks, "malankey" already means "little", so his statement becomes one about all his "little little hairs".
Alex knocks on the door of the "cat ladies" house. Later when she is phoning police she says a young man "rang the bell"