Are you using a screen protector on your shiny brand new Galaxy S4? If so let us know what kind you're using?
Personally, I have always used SGP Steinheil Ultra Crystal on my previous devices but I bought my ex, Tech Armor for her Galaxy S3 and I noticed a difference in overall clarity and smoothness... I liked it so much I ordered some for my GS4.
They fit perfectly and so easy to install. You get 3 of them and lifetime warranty. I ordered mine from their eBay store for $6.95 free shipping