Doesn't look good...
Try an environment with little dust, eg the bathroom after a shower (humidity helps),
Use sellotape to remove fibres, specks of dust from screen or protector,
Make sure the protector is the right way round (yes, there is a top and bottom for the DHD which are subtly different, as I found to my cost - I think your protector is on upside down, looking at the bottom left corner).
I have never has success reapplying protectors (apart from "during" the first application), whatever the manufacturers say. Easier to buy a new one. A lot come in packs of 2 these days
Nexus 4, ROM: Pure Speed X 27/11/13 build