Crew or equipment visible
Errors in geography
When Mary Poppins and the children supposedly go shopping before their unexpected visit with Uncle Albert, they are told by Admiral Boom to "proceed at Flank speed". A Royal Navy officer would have used "Full" speed as "Flank" is only used by the United States Navy to indicate a speed between "Full" and "Emergency".
Incorrectly regarded as goofs
At the end of the movie, the Constable described the "missing" Mr. Banks as "about 6 foot 1". There is a common misconception outside of Europe that Britain only uses the metric system when in fact they use both. Britain didn't begin using the metric system until the early 1970's. Imperial measurement (slightly different to American) is still used almost exclusively for measuring people/clothing and for road speeds/distances.
In the penguin number Dick Van Dyke's pants change to short legs and long crutch to long legs and short crutch. This was deliberate, as Burt is clearly seen adjusting his trousers to match the shape/characteristics of the penguins he is dancing with just prior to and following the scene.