Drive 17:40 Perhaps I'm being a bit picky here, and a bit of a squeaky wheel, but I'd love to get this to work. Whatever I change the Angel to it won't smooth out the holes. 
Are you referring to a course/video? Then you can always scroll down below the video, there is always a text field for questions, because then the video title is directly included in the question.
I think you created the holes with Booleans? The easiest thing to do here would be to recreate the Boolean but with a higher number of edges/vertices. SubD would probably go crazy and not work
That's because the holes are made via a boolean modifier, meaning they're not real geometry and therefore not affected by the shade auto smooth or its modifier.
If you want the holes to be smoothed you need to shade auto smooth the cutter object "hole punch bools" and adjust the angle on it until everything is smooth. The smoothness will then be transferred over to the object it's cutting into.
As Sascha and Leo said, the boolean objects themselves need to be smooth for you to see the smoothness in the holes. And of course you can always apply the boolean modifier if you want the holes to be real geometry and then you can do all the tricks to the main object itself. There are hardly any wrong ways to doing things in Blender, only personal preferences. And yes, there are more optimal ways than others, but again, hardly ever wrong ones.