Other mistake: In the ceiling tea party, Mary Poppins offers Bert some sugar, and when he responds that he would not like any, his Cockney accent is gone.
Other mistake: As Admiral Boom's assistant is loading the cannon a third time, he puts the red rocket in nose first rather than stick first.
Other mistake: After Bert and the others dancing on a railing that should have moved, as it did when they jumped off, three sweeps walk back and forth on their hands over the street between buildings. After dropping to only their toes to hold them up, you see them drop all the way down, then stand, where there was no surface in sight to do that on.
Other mistake: When Admiral Boom orders the gun to fire on "the Hottentots" (the sweeps) the rockets sticking out are in the order of a small red on top, a large green in the middle, and a large red on the bottom. A moment later, he orders another salvo, but the rockets are in the same arrangement. The chances of the arrangement being identical twice, unless done carefully, are very slim.
Answer: Most likely a variation on the "inexhaustible bottle" magic trick which has existed in various forms for hundreds of years - it relies on different chambers holding different liquids, and air holes in the bottle being covered or not change the pressure and allow the desired liquid to flow out. As the scene is one continuous shot with the entire bottle visible, this seems most likely - the air holes could be on the side away from the camera, with Julie Andrews repositioning her thumb for each colour. More info here: https://en.wikipedia.org/wiki/Inexhaustible_bottle.
Jon Sandys ★