Actually, I think that this issue is not specific for gedit, but for the save as dialog box in Gnome/GTK in general.

When you select "Save As..." for a new document in gedit, a pop-up window shows up.

My most common use case is that I first select the directory in the where I want to save the document with the mouse.
After selecting a directory, the file name (by default: "Unsaved Document 1") is still highlighted. This gives me the impression that it has the focus, however, it has not, because when I start typing, an unexpected search gadget appears, instead of that the highlighted file name changes.

I would expect that the file name has the focus, and that when I start typing this file name changes.

I'm using Fedora 23, gedit 3.18.3