The quality is low

Please answer 

Is it a part in the video you don't understand (in that case include a time stamp) or is it something you are facing while attempting the course?
From the little to go off of, I'm guessing you don't see verts because you/or the video is in edge select or face select mode.

It is in the video when he selects a vert it becomes difficult  to see

This was recorded with an old version of Blender 2.80, when x-ray vision wasn't that well developed. Nowadays it's easier to see selected vertices inside another mesh (but you'll have to enable X-ray Mode now).

That will help in the future

It is in the video when he selects a vert it becomes difficult  to see at 12min and 50 sec

It is in the video when he selects a vert it becomes difficult  to see at 12min and 50 sec

I do not know what you mean, sorry.

There is a highly visible 'manipulator',  that shows where the selected vertex is:

It's in the middle of the white circle.