Why does the Visual Studio editor show dots in blank spaces?

Visual Studio is configured to show whitespace.

Press Ctrl+R, Ctrl+W.

If you are using C# keyboard mappings: (thanks Simeon)

Press Ctrl+E, S.

If you want to use the menu: (thanks angularsen)

Edit > Advanced > View White Space

Looks like you have the view white space option enabled. Go to Edit -> Advanced -> and uncheck "View Whitespace"