When Oliver gets out of bed and goes to the window during the lead-in to "Who Will Buy?", his hair is tousled and sticking up. When the camera angle changes to the outside, his hair is neatly combed.
When The Artful Dodger first introduces Oliver to Fagin and the rest of the boys, Fagin is cooking sausages in a cast iron skillet which he then sets down on a wooden table. They boys are eagerly plucking hot sausages out of the pan to eat, but the number of sausages does not accordingly decrease. Instead, the number of sausages varies between the numerous shots of the pan.
In the "I'd do anything" scene, Bet's hair changes
During the number "I'd Do Anything" Nancy's companion is seen with unbound hair, then a half ponytail, then unbound again.
While singing "As Long As He Needs Me," Nancy's dress hangs off her shoulder and then in the next shot it is back on her shoulder.
The "Boy For Sale" scene is historic nonsense: even during the harshest phases of the Poor Laws, a workhouse pauper could not be traded like a slave from one "owner" to another. Apprentices could be had for nothing, and it was state representatives like Bumble who had to pay tradespeople like Sowerberry for the service of taking paupers off the state's hands, rather than the other way around. The book got this right.
The steps at London Bridge are depicted wrong. The real steps were narrow at the top, and widened horizontally at the bottom, allowing a person to hide and eavesdrop on (or watch) those on the upper steps without being seen. The book got this right.
In the number, "Who Will Buy", the question is asked, "Where is the man with all the money, it's cheap at half the price". Anything is cheaper at half the price. The correct statement would be, "It's cheap at twice the price," which is the original English adage.
Right before the song "Pick A Pocket or Two" starts, when Oliver asks Fagin "Is this a laundry, then, sir?", the Artful Dodger visibly mouths the exact same words.
Just after Oliver asks for more gruel and is taken by Mr. Bumble to the governor of the workhouse, they are standing at the door--Oliver mouths Mr. Bumble's lines, then to cover it up, starts wiggling his tongue.
Bill Sykes' shadow does not match his actual steps when he is first scene.
In the mess-hall scene at the beginning, the fire under the cauldron is depicted as being fueled by wood--by the scattered logs around the base, but little, if any smoke is visible throughout the scene. Also, the amount of flames continually changes between shots.
In the song "I'm Reviewing The Situation," Fagin imagines himself owning "a suite at Claridge's." However "Oliver!" is based on Dickens' "Oliver Twist," which was set in the 1830s, and Claridge's Hotel was not founded until 1854.
In "Who will Buy?", just after the schoolgirls are pushed into the pool, a family leaves a house and the mother is wearing hat and clothing more appropriate to the 1890s than the 1830s. She has on a large hat with a brim as opposed to a bonnet and her dress is definitively from a later era.
There is a pub in the main street called "The Victoria", and the post box Dodger hides behind at the end of the film is embossed with "VR" for "Victoria Regina". Oliver Twist is set in the 1830s, and was published 4 months before Victoria's accession.
On his way to London, Oliver gets onto a cart which is being pulled along a tarmac road. The first tarmac road in Britain was in 1902; the story was set in the 1800s.
The window cleaners who appear during the song "Who Will Buy?" are using aluminum ladders painted brown.
When Oliver starts his journey from the workhouse town to London, it's winter. As his travel proceeds, the winter snow melts, and the landscape becomes green. By the time he arrives in London, it's clearly summer, judging from the people's clothes and the abundance of vegetables. While conversing with the Artful Dodger, Oliver explains that he has been walking for seven days.
Fagin receives stolen trinkets from Bill Sykes just before Bill gets his supper, but there was no way Bill could have been able to keep all the stolen goods inside his coat.