The holes look to be borderline on the need for mesh tape or screen. If you go without mesh, it may take two or three coats to get it flush as the drywall compound shrinks as it dries, leaving a slight depression in the center. The mesh will help minimize that shrinkage at the center and may cut down on the number of coats. You might try the self-adhering mesh screens - they seem to be a bit thinner than the mesh tape and easier to cover without causing a hump in the wall.
Here's a good step-by-step article with video - http://buildipedia.com/at-home/walls-windows-doors/item/1388-how-to-repair-drywall
Here's a good step-by-step article with video - http://buildipedia.com/at-home/walls-windows-doors/item/1388-how-to-repair-drywall
