Visible crew/equipment: When the maid first opens the door to Mary Poppins, you can see a shadow of something, presumably the camera, on the maid's left shoulder until she steps right.
Visible crew/equipment: As Mary walks back to sit down the shadow of the camera is on her back.
Visible crew/equipment: As all the sweeps come out of the chimneys, the wires holding them are visible.
Visible crew/equipment: As Mary Poppins gets to the top of her exit from the chimney, the wires holding her are visible. And as Bert lands, his wires are visible.
Visible crew/equipment: As Mary Poppins walks over to put the hat stand in place, the shadow of the camera plays on her dress.
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 ★