How to use Boolean Operations to create Windows in a Mesh? Is there a way to make an object like this without the artifacts?
No matter how I do it, they are always there. I may be missing something.

This is a boolean operation. No matter how I approach the base mesh (the arc), solidifying extruded bezier curves or making it out of a cylinder, also for the cutter it's the same, I always end up with these artifacts.
I was having this problem yesterday. 
When you do booleans with a lot of round surfaces you can get these problems.
Check that your normals are facing the right way. Try to line up vertices through rotation or extra subdivisions and then re-mesh afterwards. Also make sure to remove double vertices.
It's also nice to have a linked duplicate, of the cut out, off to the side to modify.

As for a fix, Try this: