17 minutes into the film, Oliver is delivered for his apprenticeship and the old gentleman is holding a candle. As he approaches the door you can see an electric cable powering the "candle" being pulled quickly along by his feet.
When Oliver is in dock being tried for pick-pocketing, after the judge says "Oh stand away" the camera becomes an Oliver POV shot. Just before Oliver totally collapses he looks up to the ceiling, (and therefore so does the camera) briefly showing the full studio rafters, complete with lights, and the set microphone, and part of the "set ceiling".
At the beginning as the storm rages there are two successive shots of shaking bare tree branches silhouetted against the storm clouds. On the second shot a crew member's hand and forearm can be seen shaking this branch.
The goof item below may give away important plot points.
In the final scene, in a close-up, Oliver is holding the elder gentleman's right hand in his left, and is to his right. When they turn the corner, in the long shot, Oliver is now being held by his right hand and is to the elder gentleman's left.