Large gaps between home screen icons, can it be reduced? The icons on the Samsung Galaxy S3 have large gaps between them, enough so that if they were moved closer together you could fit at least one more row and maybe one more column. Is there a way to change this?

This is what it looks like:
AFAIK there's no built-in method to achieve that personalization.

I would go with Apex Launcher by Android Does available from Google Play Store, to use with Android 4.0+, it's free and among the features you'll find:


  
  Customizable homescreens and grid size
  Scrollable dock
  Infinite &amp; elastic scrolling
  Customizable app and folder icons
  Multiple drawer styles
  Drawer apps sorting
  Hide apps from the drawer
  Enjoy homescreen gestures
  Backup/restore settings and data
  


APEX Launcher Homescreen Settings:



Other features can be found if you go PRO.