In the sequence of "Who will Buy", just after the school girls are pushed into the pool a family leaves a house and the mother is wearing hat and clothing more appropriate to the 1890s rather than the period of the film. She has on a large hat with a brim as opposed to a bonnet and her dress is definitively from a later era.
The "Boy For Sale" sequence deviates from both the novel and history: even during the harshest phases of Poor Law reform it was illegal for the government to sell paupers as slaves to tradespeople. It was also pointless, as apprentices could be had for nothing, and the state had to pay tradespeople for the service of taking paupers off their hands (as is the case in the novel, where the fee is paid by Bumble to Sowerberry).
The steps at London Bridge are not designed in the manner that the real ones were. The real steps were, as Charles Dickens describes them, 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.
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.
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, and then to cover it up, starts wiggling his tongue.
The goof item below may give away important plot points.
At the end, Fagin and Dodger walk out of the city down a long cobblestone street. As they walk directly towards the sun rising in the distance, with their faint shadows seen following them appropriately, we also see larger, more pronounced shadows on the brick wall to their left - which is at a full 90 degree angle away from the sun in front of them.