Question: How did they film the shot with the different colour medicines coming out of the same bottle?
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.
Question: Why does Dick Van Dyke play Bert and Mr. Dawes Sr?
Answer: Because he's a talented actor who can play a broad range of characters. It's not that unusual for an actor to play more than one part in a movie: Edie Murphy played practically his entire family in the two "Nutty Professor" films. There's also a tradition in versions of Peter Pan that the same actor plays the children's father and also Captain Hook.
Question: Does anyone know anything about the word "supercalifragilisticexpialidocious?" Who made it up, how they came about to making it up etc.
Answer: For a good explanation, go to The Straight Dope: http://www.straightdope.com/mailbag/msupercali.html. It will give you pretty much everything that is known about this odd word.
Question: The very last mistake listed for Mary Poppins says that you can see the lamp post coming through the bag and the table. I have watched this scene many times (in slow motion and otherwise) and I can't seem to find what you are talking about. Could someone please explain it's talking about?
Answer: There's no reason you shouldn't be able to see it, it's so obvious, unless you have the movie on DVD. It's possible they fixed the framing of the scene for its DVD release.
Question: Does anybody know how they did the scene where Mary Poppins is doing a duet with her mirror image?
Answer: They recorded her singing in two separate parts and fixed them together. The editors did a good job on it! It may have been made a long time ago but even then the technology was quite advanced enough to carry out that scene.