Vertex Paint Issue

Hello. Can you walk us through the process? So expand on your explanations a little more. What exactly are you doing? So we can see where the mistake is. Also attach some screenshots to see if we can spot an error.

Did you assign the material to their respective faces? At around 2:55 Kent starts the process of assigning each material to the faces of the lamp post. That way material #1 is assigned to the entire lamp and material #2 is assigned to the faces that make up the glass of the lamp. And then the vertex color will work as you intend.

You can use Face Masking and Select the Faces you want to Paint (they will show slightly darker) and then use CTRL+X:

If I remember correctly, that's how Kent does it as well (but with the 'old' shortcut SHIFT+K).

Maybe this is one of those cases where we have to go deep into Sherlock mode. Can you upload your file and paste the link? So we can tinker with it and run experiments. 

That's probably because of the Lighting and the Shader you are using.

That's one of the things when we're starting to learn that seems frustrating, you can't get your things to look like what you see the teacher doing in the video. But that is not necessary, so much stuff influences how each Blender looks, it basically doesn't matter. You can have a different HDRI set up, the rotation of the HDRI, the Blender version changes the shading, etc, etc. You will get different results most of the time, and that is a good thing, you don't ant to just copy paste what you see.