How to Install Weather stripping under an Entry Door for a Tight Seal?

 

The door bottom looks fine to me. Can't really tell from the picture though. It does look like you need to scrape off the caulk where the tile meets the door and recaulk it. A sanded grout caulk that would match the color of your grout, such as what you'd find in the tile section of a big box store, would probably be your best bet.

If you need advice on the threshold and/or door bottom, open the door and give us a picture of the threshold. And also a picture of the door bottom, as viewed from the edge of the door (also while door is open).